Okay, I hope I helped in some way despite my really poorly made, complex explanations, whenever you are ready, you can leave.


You definitely helped, thanks! Have a great night!


Hellooo


Hi!


What do you need help with today?


I need help with graphing quadratics in vertex form


Ok


Is there a specific question you want to solve?


I would !like to upload it


Ok!


Let me see if I can


There!


Ok! Let me take a look at it


Could you hear me


Yes, I can


OK, that's good


Ok, so let's start at the top


I


Oh, I can hear you too.


Oh ok


Do you want me to speak or just chat


Uh, you can, you can, um


you can talk so it can be much easier for me to understand.


OK, hi, can you hear me


Thank you


Yeah. Oh, I like your voice. You're welcome.


OK, so


um, do you just wanna start at the top.


Uh yeah


OK, so do you know the equation of the graph at the top.


Uh


which equation


Like it says the parent quadratic function is.


Oh yeah


OK, so do you know what the apparent quadratic function is.


Uh no


OK, that's fine. Um, so basically, it's F of X equals x squared.


Now, let me type it


f(x) = x²


So that's what the parent quadratic function is.


And basically everything below is just transformations of the parent quadratic function.


Does that make sense?


Yeah


OK


So


um, the U-shaped graph of a quadratic function. Do you know what that's called?


Uh, parabola, parabola, right?


Yeah, parabola


Um


and then the line that divides the parabola into two mirror images. Do you know what that's called?


Axis symmetry.


OK.


Yeah, OK


And then um the point at which the problem meets the axis of symmetry. Do you know what that is?


Yeah.


now for the first one, it's a reflection


so


basically


um, since it's negative, it would be a less than 0. So if you add like


um a reflection is like a negative sign. So if you add that, it just flips the parabola.


Does that make sense


Do you have an example? sorry.


Oh yeah, that's fine. Um


OK, yeah, I can show you an example, one sec.


I can just like do it below.


OK


I'll write it down also.


OK, um, wait.


Wait, actually, I think the thing below it is the example. So like, um, if you have Y equals x squared or no, if you have Y equals x^2, and then you add a negative sign, so it becomes y equals x^2 + 3, then it would flip the parabola upside down.


Like, does that make sense? Like, basically at the top, you have um Y equals x squared, and then in the place where it says Reflection, you have Y equals ax^2. So it like flips the parabola, so now it's upside down. So basically like reflects it.


Oh, OK, OK.


Yeah. So it would be


um A is less than 0. And then a stretch is


um, basically, it's a vertical stretch, so if you add, like, before the x squared, if you add like a number, like 2, it would make the parabola like


you know, extra stretch closer to the axis.


Um, and that's called a vertical stretch.


So if it's a stretch, it would be a greater than 0.


So, like originally the dotted one is Y equals x squared, and then Y equals 2x2 would be a stretch of two, so it like stretches the parabola toward the axis. Does that make sense?


A little, yeah.


Yeah, um


I think it might make more sense what we, once we do the examples that basically if you add like a number um before the X squared. It's called a stretched, and the number has to be greater than 0.


OK, and then a compression is basically the number has to be between 0 and 1. So it


um, a compression is when it moves farther from the Y-axis. So like you can see it becomes wider.


So basically, if the numbers like


between 0 and 1, it would become wider.


Does that make sense


Yeah, I get it.


OK


Yeah. Um


so


do you just wanna do the example, or if you have any questions, you can ask that.


Yeah


Um


I have


yeah, what were you saying


is it


um


you and I, so I cut the screenshot doesn't show like the other half, but I have the other screenshot.


OK. Yeah, that's fine. Maybe you can just put like the other screenshot.


OK. So for the first one,


Y equals -x squared. So how do you think the parabola would look?


I think you add like, since there's no other numbers, but like, uh, negative x squared, you add like a 0 and like a 1.


like a 1x and then square.


Yeah, yeah, it would be Y equals -1 x squared.


So like on the graph,


um,


like, how do you think the parabola would look on the graph.


like plotting


Yeah.


Uh, I think you start by, you start by, uh, 0.


Yeah


underground


Um


and then


and then you moved.


you move one.


down like to the left.


yeah


OK. Yeah, so, um, to graph it, we can just like


uh start


um plotting like the points. So,


um we can start with X equals 0.


So if X equals 0, what would Y be?


so X equals 0, we can just like


um if we have like the X value and we wanna see what why is. You can just plug it in.


So it would be like


we just plug the 0 in instead of an X. So,


um 0 times anything is 0.


So, basically,


if we did hear 0 times 0, it would just be 0 and then 0 times -1 would also be easier.


So what would the Y value be?


Yeah


Um, OK. So basically, the first point would be 00. OK.


Yeah, and then


if we have one, what would 5 be?


We live to get um


we to get um one positive one from.


Um,


oh, where did I get it from?


Um, so, basically, I'm just trying to grasp the parabola, so I'm just like choosing random like X values, and then I'm trying to figure out what the Y value is. So if, if we have an X value and a y value, we have 1 point. So then um if we have like a bunch of different points, we can graph therabola. So I'm just like choosing random numbers to find the points.


Oh, OK, OK.


Yeah.


So


um, I'm just choosing Xalues and then if you have an X value and you want to find what y is, you can use the equation, so you can just plug in the X value, and then solve it, and then you can get the Y value. And then if you have X, Y, you have a point, so you can just graph it.


OK


So, um, if we had


if the X value is 1, then what do you think the Y value would be?


Uh, negative 1.


Yeah, so then we would have one common negative one. So then that would be over here.


OK. Um, OK, now let's do


Um


so if we add 2, then what would the XB?


negative 2


Um, so,


because the equation is squared, we would have to do 2 squared and then multiply it by -1.


Oh it's uh 4.


22 is 4, but then it's negative 22.


Does that make sense


I


No, I'm sorry.


Oh no, it's that. Um, OK, so basically, um, like,


we're just like


trying to graph it


So we have like


wait, yeah, we have um like different points to graph on the graph. So, um, I'm trying to find like what why would be if X was 2.


Yes


So you see how like the equation is Y equals -x squared.


Yeah


So basically


like let's say X was 2.


then um instead of wait,


oops, OK. Instead of having Y equals x squared, we can um have Y equals -22.


and then, so it would look like


this. Wait, can you see like the writing below.


Yeah, I can see, I can see.


OK. Yeah. So basically


um we would have Y equals 22, and then we're just trying to simplify it. So 2 squared would be 4. So then we would have -4. So then why would just be negative for it.


Does that make sense


OK, just um ask me if you have any questions.


OK


So, um, then we have 24. So that would be over here.


OK, so, you know what the axis of symmetry is, right?


OK. So


um


where would the axis of symmetry be here?


Like


the 0


Yeah, it would be at X equals 0.


So it would just be like in the middle for this graph.


So basically the axis is symmetry is like, it means that any points on the right are just like


um symmetrical to the points on the left.


So since we have points on the right, we can just do the same like points on the other side. So like this,


and then um once we have enough points, we can connect all of them and then we have the parabola.


So.


it'd be like this


So that's basically how the graph would look like.


Oh, OK, OK.


Yeah


Mm


So, do you have any questions


OK


No


OK.


which um


yeah, let's try the other one.


OK. Um, we


I think I understand a little bit.


OK, that's good


Um


OK let's just try the other.


OK, so now we have F of X equals 3x2. So basically we can, we can just do the same thing. So let's say X was 0, then what would Y be?


Um, OK, wait. I think it's like easier to write the equation out.


So basically we'd have 30 square.


So


what's 02?


Yeah, and then it's 0 times 3.


Yeah, so basically what I would then be there.


Do you have any questions


Um, I'm just at home. I have to write it down


OK, yeah


OK, tell me, like when you want to move on.


OK


E


Oh, I did that by accident.


OK I'm them


OK, yeah, it's fine. Um, OK


So now we have the 0.00. So we can just graph, like plot it on the graph, so it would be over there.


Um, and then we can find another point. So, for example, one, something, so this would mean X is 1, and then we would have to find the why. So,


um,


if X was one, then what do you think Y would be?


Yeah


Let's see


OK. So then you would have 13.


Does that make sense


I


Oh, you're just putting random numbers onto the first side, like the first number.


Yeah, the first, yeah, the first number is the X value. So it would be like everything on the X-axis, which is over here. So I'm just like choosing random points on the X-axis and then we can find the Y one and then we can plot the points.


Oh OK


OK. OK, thank you.


Yeah, OK


Um


And


yeah


OK, so basically we would have 13, which should be over here.


OK. Does that make sense?


Yeah, I understand it


OK, that's good. Um, OK, so now I just find like one more point. So maybe to


mama something. So


I'm sorry


it's fine.


Mm


OK, one sec


OK


OK. So,


if, I mean, if X was 2, then what would Y be?


So it would be like 2 squad and then you multiply it by 3.


Does that make sense


Yeah


OK, so what


OK, so what is 2 squad?


Yeah, and then 4 x 3.


OK, yeah. So basically, why would be 12. So you'd have to comma as well.


Does that make sense? or do you have any questions?


Yes.


Yeah, um, it makes sense. It makes sense.


Mhm


So


um, if we try to like graph to 12, it's like outside of the graph because 12 is like pretty big. So,


um I don't think we can grasp that, but we can just graph the points on the other side. So


the axis of symmetries, like in the middle, so um


we can just like plot the same points and then you can like draw the para


bo


Wait, what? I'm sorry.


Oh, that's fine. Um, OK, so you know the axis of symmetry, right?


Yeah


Yeah. So, um, where would it be in this graph?


At the serum


Yeah, so


um, it would be like in the middle, and then


yeah


but the


remember how I said like


I'm sorry, I'm sorry.


Oh no, no, it's fine. Do you have a question?


I was gonna say like the the uh the axis sym symmetry is like in the middle, like the street line, right?


OK


Um, yeah, so for all graphs, it's not always in the middle, but for these graphs that we're doing, they're in the middle.


Yeah.


Um


so basically, for the axis of symmetry, the points to the right of it are like.


symmetrical to the points on the left. So we can just draw the points that are symmetrical, so we would also have a point over here. Does that make sense?


Yeah


OK. And then, since we have like enough points, we can just connect all the points and then draw a parabola.


So we could just do like something like that.


Does that make sense?


Yeah, it makes sense.


Um, OK


OK. Um, we can just do number 3 now.


Mm


OK. So we, we can just do like the same thing. So let's just start with 0.


So


so if X is 0, then what would Y be?


Uh, I think it's, uh, 33.


and


Mm.


So,


OK, what would 02 be?


Yeah, and then basically 0, it would be like 0 times 1/3.


but 0 times anything is just 0. So it would just be 0. Does that make sense?


Yeah.


OK, yeah


then we have 0.0, which is the first point.


Do you want time to like write it down


Yeah


OK, and ask me if you have any questions.


OK


OK, I'm good


So now let's do


one something.


So if X is 1, what would y be?


Uh, when


So this is like a bit more complicated because it's a fraction.


So first, what would one squared be?


Uh, one square is one.


yeah, just one


Yeah, so then we'd have to do 1/3.


times 1. So what would 1/3 times 1 be?


One


Um


so


OK.


basically, if you have like a number,


the number is equal to that number over 1. Wait, let me just show you an example.


So like if you have 5,


5 would be equal to 5/1. Like it's like the same thing. Does that make sense?


Yeah


Yeah, so basically I have one here. So one would be the same as 1/1.


And then if you're multiplying a fraction first to multiply the numerator and then you multiply the denominator. So what would 1 times 1 be?


Uh, one


Yeah, and then what would 3 times 1 be?


Yeah, so basically 1/3 times 1 is just 1/3.


OK


Yeah.


OK. Um, so then our next point would be


um


Oh, let me write that down.


OK, yeah


All right


OK, great. So now we can choose


one more point. Wait, first let me graph11/3.


It'd be like over there


Um


So it's in between


huh


It's in between the graph, like in between


days.


Yeah, um, basically, um


each like


we're graphing it so that each unit on the graph is one. So basically, this would be 0 and then this is 1, and then 2


456. So since 1/3 is like between 0 and 1. it's gonna be like between


like this, um, between both of those points. Does that make sense?


Yeah


OK.


OK, so


Sorry


um, OK, now let's choose a new point. So


let's do


um 2


something


So,


um,


now X is gonna be 2. So if X is 2, what would Y be?


Um


uh


is it the same thing, same thing like uh last time.


I was gonna.


Oh yeah, it's always just like.


Yeah, what were you saying


uh, I was gonna like say 4.


because I'm too squared is 4, and then


I think you, you said multiply it.


by


No


That I might be wrong cause I'm not sure.


Yeah, you're right. Um, it's like


Yeah, it's um 2 squared, it's gonna be 4, and then since this time you're multiplying it by 1/3 instead of 3, so you do 4 times 1/3, and then you get the answer. So


um, what do you think 1/3 times 4 is.


Yeah, that's right


Mm


Oh, OK. OK.


It's just like one times 4 is 4 and then 3 times 1 is 3, so.


OK, OK.


yeah, so you would have to


karma for 3 and 4/3 is like


an improper fraction, so it would be the same as 1 and 1/3.


So you'd have 21 and 1/3. Does that make sense?


Yeah


OK


Let me write that one down to.


OK, yeah


And then wait


Oh never mind


Um


OK, so now you have 2 and 1 and 1/3. Do you have any questions, by the way?


we are he's just like, OK, so the other, the one that


can I like circle your


Yeah, you can


eye


I don't wanna mess up your um


It's OK.


I don't wanna miss anything out though. OK, let me try


It's OK


I I


We can just like fix it later.


uh, you put this into like


oops


OK, so the one that I circle, you just add it to the end, the answer that we just did.


Um, no, wait, so, basically we have 1 1/3, which is


this point that I graph. Do you see that?


Yeah


Yeah, so then we found um a new point. So basically, it is 2 4/3.


um, and this is like the new point, but I just um wrote 4/3 is in like improper fraction, right?


Mhm.


So I just wrote 4/3 as 1 and 1/3.


So 24/3 is the same as 21 and 1/3.


Does that make sense? Like, there's still


like both of these are like separate points.


Um, this is like the same thing as 2 and 24/3.


has


one


and 1/3


yeah.


It's like um uh like,


mixed fraction


I understand it a little bit.


OK, wait, um


OK, so basically, we found um 1 1/3 by like


using the one as an X, right?


Yeah


Yeah, and then we got like that point.


And then we basically wanted to find two, something.


So then that's what we did below, right?


Like the


ones on the left are the X values.


So first we did X is 0 and then we got Y is 0, so we're like.


choosing different X values and trying to find um a


Y value for each one.


So first we had 0 as our x value.


And then we um plugged in the 0.


and we got Y equals 0.


right?


Yeah, and then we did the same thing for the one, so we did.


Y equals 1/3.


times 12, and then we got 1/3, right?


Yeah, and then we're doing the same thing for the two, so we're doing Y equals 1/3 times 22. And then remember how we got 4/3 for that.


Yeah


So then that would mean that this point is 24/3.


Right.


Yeah, yeah. I understand. Yeah, I understand.


Yeah, so then basically what I did is I just did


like 4/3 is the same thing as 1 and 1/3, like it's equivalent.


to that.


OK


So then I got to comma 1 and 1/3. Does that make sense?


OK.


So


you, sorry, you


you just, uh, OK, so the, the, this is a 2 is the X of the um.


2 is the X.


yeah, 2 is the X of 4/3.


And then you, you just put, you just find any number on the on the graph, like any number on the X.


Um


value


Yeah.


OK, I unders. OK.


Yeah, you can, yeah, you just choose any number on the X axis, and then we can find a number for the Y.


OK. Um


so


then we can just


we, we can just graph 2 and 2 and 4/3.


So then we would get the point over there.


Does that make sense


What did you say? I'm sorry


Yeah, um, so I just graphed the point 24/3.


Mm


Like a graphed the point over here.


Wait


over here


All right, good. Oh


OK.


I, I plotted it. I plotted it on the graph.


we


uh, which point is that?


Um, it's


so this is


this point


over there


And then you point me to for like between 43, we went to x and y between 2, right?


Yeah, we plotted it.


OK


Yeah.


OK. Do you have any, do you have any questions?


No.


So


now


we can do the same thing with the axis of symmetry. So where would that be? Here.


Sorry


It's


What, what, what was your question?


Um, so where would the axis of symmetry be here?


Remember like the um online.


down the middle that


we like the um


the points were like symmetrical and everything.


Uh, at the 0


So then


we here


I'm just looking for


Yeah, what were you saying


I have notes from my school. I'm just looking at my notes so they can help me on it.


Yeah


OK


Is that OK


Yeah, that's fine


OK. Um


so now we can just


plot the points and symmetrical.


So, the points on the right would be symmetrical to the points on the left of the axis of symmetry.


So


you would


it would be like


over there. Does that make sense?


So we just copying


the other side


OK, it makes sense.


Yeah. OK, and then we can draw the parabola.


through all of the points


So it'd be like that


Well, I think I understand you a little bit.


OK, that's great


Um, OK. Do you have any more questions?


Uh no


OK, great


Um


hm.


OK. Are there any more problems that you wanna do?


I was gonna do some tomorrow, but I'm not sure if we're gonna like have it together to um


again with they said um on the website it said I can like


um make you my favorite.


So in the future, you can come again, if that makes sense.


Oh yeah, um, you can, yeah, you can like, if you favorite me, I think that.


I will like get all of your requests.


Um, so you can do that and then if we like, if I don't get it, then I can message you myself.


Message me


Yeah, like on the website, um, I can


like, you know the chat that we have here.


Yeah


Yeah, I can like, um, you can like


go back to like your old chats, so I can message you on this chat too.


Yeah.


Oh, that's cool. OK.


But you should probably like um


so if you favorite me, and then tomorrow you put in a new request and I'll probably see it.


OK


Um, OK. So, are you like gonna do that around like the same time?


Like now, I would do it after. I'll do it when


when we end this session, I'll do it.


Oh yeah, but, OK, wait, so you wanted to do the other problems tomorrow, right?


Yeah, that, the other problems is um


uh ex graphing graphymo points.


OK, yeah. So tomorrow, do you like just wanna um do this like at the same time.


Yeah, at the same time it'll be fine.


OK, so maybe you can like put in a request around this time, and then I can check.


OK.


I'm gonna do more, I'm gonna do more practice problems on my own, to see if I can get it.


Yeah, OK


All right, thank you so much.


OK, yeah. You're welcome. Have a great day.


All right


Thank


Have a good night and good day.


OK. OK, you too. Bye.


Bye


good morning


where are you located, i'm in Houston


what is the problem you are working on


hai


im from  Seattle


and i have a problem/ assignment


this is a sample solution


we do f-h\


but different like


ano


dimensions


what problem are you struggling with, should we turn on the mics


Ah, and


I


we


you know, hi, the notion that we were given was basically, wait.


I lost it. I had a screenshot of there's a why is it so lucky. 0, 14 by 13. OK. I guess we do have


OK, uh,


yeah


OK


hold on a minute, hold on a minute. OK, so, um


you got 2 sheets here. I can't kind of read. OK, you have um


sketch the rectangular material, I can see 10 inches by 6 inches.


Um, but like where the box is like part C. I can't really see the labels here. Um,


Yeah, see, I can't.


Can you zoom


OK, I'm going to try to, wait, where forboy. Oh, we don't really, uh, oh, we don't really mind cause my partner already did this. I will just like we will just prioritize doing the like the solving for volume until sketching cause my partner, they did it, she just needs confirmation because she was uh kind of


paranoid and are like.


the thing that we're now wait,


the.


oh my, why is the deadline next week. It's 14 by 13 inch.


OK, I think we can.


OK, just maybe zoom in on the problem that you want me to solve. That way you wanna work on.


OK. Uh, we just use like the


like the polynomial, so it becomes the of Sarah. It's just like 14.


14 minus 2 x 1314 by 13 so to go, yeah, 13


minus 2 X.


then


which


OK


X now, then we, we, the thing that I said, we solved it to become a polynomial, and then we, then we find the zeros of it and then we use, we find the turning points of the graph the using the quadratic formula, and then we do substitution in a way. OK.


OK, so


Let's cook. So the first thing we have to go.


yeah, the. I'm, I'm sorry.


uh


OK, so I see you, you look like you have this so for the zeros or 03, and 5. I'm just looking at your sheet.


Um


Nope


now, what's uh, so what is the problem actually? What are we, I'm still not sure which, which you


Oh, the problem, what we're gonna do is basically our math teacher, our Ms. Davis, she gave us like a set of dimensions, and then we turned those dimensions and we make it into a graph and then our teacher just said to make it into the, to like the solution, we just have like the length and the width minus 2 X is like the function that I gave earlier that I texted.


Yeah.


uh, OK, so, so let me understand. So you, you, what you, what you put in front of me is exa is an example for a rectangle 10 inches by 6. But now you're gonna, but now you have a new, you have a new dimension and you want to rework this problem with new dimensions. Is that right?


Yes, this is like a reference solution that our teacher wants, and this is kind of like our, our big project that's due next week because we're gonna use a dimension that we just had and we're gonna start is gonna our Ms. Davis is gonna give us, give us the X so that like we could actually construct the box, but our teacher wants us to prioritize the graph graphing until next week. I think it's like due on Tuesday, but


uh it's good that we did it early cause this was given yesterday. I'm gonna speak, let's speed run this.


mhm


So


All right. So do you want to work through this problem with new dimensions? Is that what you wanna do?


Yeah, I get it


yes, that's basically what our teacher wanted to do, and this is kind of like me, what the heck? This is kind of like the sum this kind of like the sample solution that they sent and this is a picture of like my


this is kind of the picture that I had cause the sheets actually with me.


I have it with me


OK


as you can hear. I'm just gonna


gonna get


I'm gonna copy


This


and uh learn from this so the polynomial function that monos the volume of the box. So, uh,


we just did


so what we do is the, oh God, why is it falling? We do the anno, right? Oh my god.


OK, uh


We do the thing that I sent, like the 14 minus 2 x, 3 minus 2 x, and x, if I'm not mistaken, but


Yes.


Yeah, I think we, let's, let's make some draw. Let's do some drawings together, OK? And


OK.


let's, let's, uh, what, what's the, what's the size of your paper?


Uh, the, the size of paper that we have is a short sized one, I think it's a letter, letter sized bond, but sir, our miss actually, uh, doesn't mind what she's the paper that we submit and as long as it's just a square of a box with the correct labels because the actual like box that we're making is next week


Yeah, so let's start.


We have the box. I'm drawing the box.


OK


Where's the, uh, where's the where you draw all you're down there drawing it. OK.


Yeah, and, and then um. So


as like


earlier


we have the


I'm very, very


Yeah, you got to cut out


Yeah, and this is kind of


Those are, are those supposed to be squares you're cutting out.


Yeah, yeah. I'm gonna make it more accurate when uh


Yeah, that's, I, I get it, X and X, yeah, yeah, yeah, OK.


Yeah.


X and X and wait, let me see, the thing that I sent for


was.


14 minus 2X.


2 X, yeah, yeah.


minus 2X.


OK


OK, so your paper, your paper is 14 by 13.


Yes


and you're gonna make a box


that's uh


sure.


Yes, we're, we're gonna make a box out of this. So what we can do is that we do this with polyfunction, so 40 minus, I'm gonna solve this in my iPad and I'm gonna, I'm gonna tell you my answer and if, and let's compare.


So are you trying to calculate volume here.


Yes, actually, yes, yes, we're gonna.


volume of the box. OK, so what's the, what's the formula, what's the formula for volume?


oh, without looking, LWH


Yeah, I mean, it's the length times width times height, right?


Yeah.


With them height. Yeah, OK.


So break down the


Uh, this is just basically uh multiplying polynomials. It's OK. I will speak and.


yeah, so what's your, uh, so write, write down your formula for if I did this V


of X


So your formula


Yeah


for the volume based on X.


is equal to what?


2 x


14 times 1314.


15 times.


OK


Mhm


right? What's the next factor?


right


Uh, 13 minus 2x trying to also do it myself. I have a calculator with me right now. 40 times 3, it's easier when I do it in


OK, what's the next, what's the other factor?


An X


That's right. OK.


Let


OK, let's go on. 40 times 13 X and 14 times 2 is 28, and since the act.


Well, let, let me ask you this. Why, why do we need to, um, what are we trying to do with this volume? I, I, are we trying to optimize something or what do you wanna do?


yeah, or tried to optimize this so we can find the 0 so that we can transform into a graph.


as seen in the 2nd.


OK, well, we, we've already, OK, this box right here.


don't, don't we know the zeros of it already?


Oh, but that's a required thing that they want.


on form.


See what's the um there there's 30s here, right? How, how does, how can VFX equal to 0. Well, this could be 0.


What does, what do you need X to be for that to be equal to 0, the first box.


What? Can you rephrase the statement, please, 21.


Mm.


OK. All right, let me, let me undo this, this, um,


I'm trying to find the zeros of this


polynomial, right


Yeah


OK, so in order for this to be zero


uh, a couple things


OK, let me, let me switch colors.


Mm


This factor could be 0.


right? Or


this factor could be 0, right? Or this factor, you see how there's 3 parts, 123.


What, what is the 0? What makes this factor zero.


How does 14 minus 2x, how can that be equal to zero? What is X?


Um


For it to be 0.


for


um


if you make to 0, it would still be 14.


It would be, if you subsequent


OK


No, no, no, no. I say, how, how do I make, how do I make 14 minus 2 x equal to zero. I want the whole thing. I want this, so I want this.


minus


2 X.


to be equal to


Oh, that's gone. We transpose you to additive inverse, additive inverse method. Then we did then we divide it.


so positive to x over 14, and then we just divide it so x equals 7.


Yeah, OK, so X equals 7 is a 0.


Oh.


OK, so you just said X equal to 7, that's 10.


right?


Yeah


Oh


You see that if that's equal to 0, then that'll be, it forces the whole thing to be zero. OK, what's the second? What, what's, uh, how do I make this, this factor equal to zero. Same thing. 13 minus 2 X.


So 2 X divided by 13 and oh, we just flip it. It's 13/2.


We don't even need to solve. Oh, OK, um.


I


Yeah, so that's X equal to 6.5, right?


Yeah, 6.5.


OK


Or you could say, yeah, 6.5 or 13.


Did you actually doesn't mind if we answer it infraction, but she said the play it safe, you can just add the decimal or in the fraction to to play it safe.


OK.


Yeah, so you, you could say at 13/2 or 6.5. OK, what's, how about this? What's this? How does X equal to zero? What's that?


X equals 0 cause you can't transport, you can't have to additive inverse.


OK, so


props to organic chem through their doer for teaching goodness. I, I actually


more


so this is, you know what a 3rd degree polynomial is.


Yeah, a 3rd degree polynomial and it has a degree of 3 when its power is 3 fe'm not mistaken.


Right. So this, so it has 30s. So we found the 30s, right?


Yeah


continue


So now what do you want? I'm, I don't quite under what, what do you wanna do with this? You wanna graph it?


Uh, essentially


yes, but then we have the table of values, but then we have to find uh the turning points of the graph.


We essentially have to find the turning points of the graph. Like turning points of the graphic letter G, we essentially do from what I've understand like the quadratic form, the quadratic formula, and then after that, we use those answers and we substitute it to the formula that you originally get from the polynomial function that you being solved from the 14 minus 2 X and the 13 x min is 2 x thing. So we actually have to get the formula so we can substit


ute it.


We have to actually get.


See, I don't know why you need the quadratic formula because we've already got the quadratic formula finds the zeros.


We've already found the zeros, right? Boom.


Oh, but the thing is, what's here is to find the turning points of the graph.


We already have the extra, we need to find the turning points and


we need to use


oh yeah


Oh, so you're gonna take a derivative. Oh, you want to take a derivative. All right. So you want to find maximum points.


Are you doing little calc you know how to take a derivative? Is this calculus?


Yes, this is a, this is AB cup where this is like our AP family.


Oh you, oh, you're an AP count. OK. OK, I used to teach that. All right, so you want to find the, uh, what I would call um the minimum and maximums.


Oh yeah, I do know what the meaning of a maximum is.


OK, so you're doing, this is AP calculus. All right, so you're trying to figure out what the maximum volume in the box could be.


yeah


OK. All right. So, all right. Well, that's a whole different story than now, so you don't really need the


you know, this, I mean, you could put 0. 1st of all, let's, let's, uh, can you multiply out via X and then we'll take a derivative. Or do you know what the product rule is?


Yeah, but like our sir asked us to find the turning points of the graph and finding like the X for the X coordinates for each of these points by using the formula and I think it's the best way that we follow, we follow the formula along, we follow this.


OK


All right. Let's see, let me look at what she saw.


volume


the zeros or X intercepts. All right, so we found the zeros. All right. Now let's multiply out via vaccine.


Let's, let, let's multiply that. Once you multiply that out.


Uh, I have it in my notebook. 14 x 13 X to 14 minus 2 x is 28 X, and 2 x 2 x times 3 digit.


OK.


Well, well, let's just, can you, uh, can you write it down? Yeah, I, you know what, I have a special


I just, let me try my stylist here, and I'll write it down so we can see it. I think I


I had trouble writing with my um


Um,


I have trouble riding with, OK, let's see it here.


40 times. What's the special, oh my God, I hate this house. 14 x 13 X. 0 my God.


Yeah, here, let, let me, um, if you, if you gave me this, uh, well, I'll tell you what, you put it down. I'll, I'll calculate it too.


I


s


um


this


14 times 13.


So negative 50


5 X. On ale


It's not 3.


Oh


and then you had an X.


Oh.


and


Hmm.


Wow


What's 14


it's


Mhm.


What'd you say 14 times 13 X.


Oh, it equals


It's.


Oh yeah, 182


minus 27 X plus.


4 X


So it's gonna be


Mhm


OK.


OK, so what was your


Hm, I'm not it


what was your answer? Uh, it should be.


it


let me do this cause it's a hard trouble reading. Um,


but


is that, uh, are you getting like


uh, cute.


minus 27 X.


you like, and so my hands so I can. I'm not yet done. I, I only have the base like for the for the what they call again for the


uh


I only have the one for the foilat and I did not multiply it with axia, 4x2positsia, I mean, why am I speaking my native language and I stress. OK. Uh, 4 X cubes minus 54 X^2 minus NO + 182 X I correct?


I will write this. 4 X raise a power of 3 minus 54 X^2 54 x squad.


U


OK. I don't


you to um.


I don't have 54X. Let me, um,


whoa


let me redo this then


I, I have 27, I have 27X. I don't know.


like 26. I have 54 cause like when you multiply 14 times to x.


It's negative 28.


Oh, you're right, you're right, you're right, you're right. You're absolutely right. 54, you're right.


You you are correct


Oh yeah, OK.


OK, well, let's um


They are coolly. OK. The next part is since we already have the formula and then we just extract the zeros.


let's make sure we, let's write down the formula for volume. Let, let me see if I can do this.


4x^3 -54x^2+182x


I got this uh pad here. Let's see how this works.


Um


OK, let's go.


OK


OK.


I go up here, I'd say V(X), oops.


Nope, that's not working here.


Is that you oh


Oh my God


Mm


And


then


Mm, my thing's not working. Let's see.


uh, it's OK. I will do it.


Oh


oops.


I will do it, where is the formula, or X-rays to the plow up the minus


X. 820.


So then maybe help


Yeah. Yeah, that's right. That's correct.


based from this like, since we already have the formulas at the zeros, what we can do with the, this uh formula is that we can make it into the quadratic formula.


We can, we can quadratic, we can make the formula to sign.


Yeah


Well, first thing you need to do is take a derivative of it, right? You're trying to, if you, we know the zeros of the graph, we know it


Now we, if you want to find


you know, the maxes and men's are gonna happen right between them.


But


how do you take


I think your paper up here said


yeah


first therariation, the the variation. Oh my gosh.


Yeah, so you take a derivative.


The thing was, I remembered our our teacher submitting like uh, like from a shared like classroom from another like uh from another class that had APA. They had this, they had this thing like the shared like like uh like what do you mean 3rd grading recorded, uh, for this


but then I can't find, I can't find the file that had


had had this, wait, uh, let me find the dress.


Does this notation, let me ask you this, do you know what this notation means for derivative.


find the


So if I go, I want you to take the derivative, right?


Yes


Do you know how to take the derivative of this function.


uh, I, I, I know it cause I seen my teacher done it, but I'm not that confident doing it in school.


OK, I'll, I'll show you. It's called the Power rule, right?


one the probably


So I basically


I take the, I take whatever so I take


the power roll says I take whatever power is. I multiply it out front and I reduce this. So this becomes


times 4


X


OK


yeah


So, you know, the power role.


Power roll is the following. If F of X


this is really the only, there's a lot of diff F ofvax.


Yeah


You do you know what F of X is? Like a functional notation. Are you comfortable? OK.


Yeah.


If uh if E of X equals X.


to the N


right


F


E


Oh, wait. Oh, this is like what I


um


F of X equals N


right? The N comes down


times X


you know


times N


minus 1.


So that's what I did over here, right? I took the 3


Oh


put it out front, but I have to multiply it by the 4, then I took X^2, right? So that's gonna be.


so this is gonna be equal to 12.


x


Oh, well X^2.


Oh.


2. OK. So what's the next um what's the next factor?


54 x 2. So it's uh from what I've understand negative. We, my nose, we have


times 54 and 2 minus 1 is 1, so it's just two times 54 and


2 times 54 X.


Am I correct


Not, yeah, yeah, yep, so that's gonna be minus


100 and


And then 182.


OK, what's, uh, what, what happens to X?


X becomes a 1 because it it was a minus.


No, it goes from x, it goes to X to the 1, right? Because


Yeah


it was suggested


next to the one goes to.


no X^2 becomes X, right? 2 becomes 2 minus 1, so this should be X, right?


Oh yeah, I forgot. 108, I, I forgot, but I did follow the rule now X becomes one.


one


OK, how about do do this next factor. What 182X become?


Um


wait


OK about it. There's nothing really much to wait, I mean.


think


It just becomes one.


and 182


then X-ray 1 minus 1 to 0. So it's just 182


Yeah, what's what's X to the 0 equal to?


uh


X-rays the part of 0.


Yeah


is basically, wait, let me think. It's just 0, so it's just cancel.


No


Now what's up? OK, actually, let me do this. Think about this. What's um


here


I'm trying to get my stylist back. This is.


this is a little hard. OK, what's um


is it


let's do it this way. I wish I could


Let's just


Yes


is it basically become 182, because when I need 2 times off, I knew it.


Yeah, because X to the zeros, they go to the 1, right? 2 to the 0 is equal to 13 of the zero secrets, so it's 182, right?


OK, so this


so now we got the derivative.


OK. Since we have this, we can do the one.


Yeah.


You can finally do the formula. Finally,


There's 12


There's 12 go X^2.


Anyway, you can do the quadratic formula, but


it might be easier if you factor out a 12.


This 12 times 10. It's not, no it doesn't. No.


You're just gonna have to do the quad, you can do the quadratic formula and find the zeros here.


What's the difference for X_1 and X sub 2.


like


how


it's basically the same deep plug and the same things. How do they get like different answers to have.


Let me see.


I don't know X of one. I, I don't know what you're talking about. You mean to the power.


No, it's up in


it's, yeah


It's, there's a in the solution, I know, for the solution of huge choratic formula to determine the x guardian of the of the of the each turning point and then uh above the substitution for saltfur white, there is 4.12 and 1.21.


So that's what we're trying to find.


Well, OK, we're trying to find the zeros of this derivative, right?


And what's the


what we


Oh, it's, it's just the same thing, but they, ah yes, the evil twin analogy where you just change this, oh, OK, you just did that, but you changed the signs, OK. Let's do this. OK, what is RB equal to. value?


-108 + minus


No, wait, wait a minute, what is um what is B equal to?


So


Is it negative or positive?


Z


Yeah, what's B


B is negative. RB from the ABC, B is -108, so it will basically become like positive.


OK


Yeah


I, yeah, from negative multiplied by riety of negative is positive. Is there say the positive and positive trans negative is positive. Uh,


OK.


Yeah, I'm just looking at the uh


That's it. I'm gonna write the formula first.


right, so it should be it's negative B, so it should be 108, not -108.


Negative B plus or minus.


Yeah, wait, negative B plus one. I'm gonna write the form that I want B square minus 4AC over


Yeah, 2A.


2 weeks34C.


like


Oh my God


I think the whole thing's over 2A, not just the uh


square root, right


I, I can't. OK. I give up


I just remembered that, uh, the plus minus thing because I think of it kind of like an evil twin where it has two answers. Now, it will be plus the square root and plus the minus RB is 1-1, 0 my God, I.


Yeah, those are big numbers.


That's it. I'm, I'm, I'm using, I'm using this. I'm using the system.


Yeah, 108 2 minus 4AC.


for


Yeah.


What's a, so B, B is 10 at minus 108, right? What's A equal to? What's A?


It is 12.


12, and what's C?


C is 182.


182, right.


I had an advanced, like, like


we had this in our Junior year. I kinda took uh kind of took a kind of loaded on my AP last year's for for this.


um


and


Yeah, these are big numbers


On I only got one.


of over


I know what the answers are.


He


well


I want this right.


Uh, 2 x 12 is 34.


I can write down here.


OK, that's it. I'm using this as a cycle


So


I remember 108 gets divided by 24/2, right?


yeah


Yeah


The whole, the whole plant, I can't.


All right.


Yeah, the whole thing is divided by 24. OK, so negative 108 squad.


is


Yeah, it's so they


use


11,000. 0 my God, I'm gonna do it straight -4, 12, and z is negative20. 0 my god, 20,000, 2,000,400. Can you confirm this for me, please?


I am having a psycho. If you have a additional calculator, can you check it for me please?


Um, well, first of all, first of all, when you put in a, it's the whole negative 108.


uh becomes when you square it, it becomes a positive number, right?


So it should be -1082, but negative times the negative is a positive, so.


There's a class of food.


so it's really, I, I get the whole thing as being 29


Um.


So you're, you're having two negative numbers, nega. This is a, this right here


Mm


That's a positive number.


I'm gonna redo this. Oh, it's 4384. I had another, I have another answer with my, with my psychar right now. I probably did it wrong. I did not, uh, bracket it correctly.


Yeah, sure.


Can you recheck, can you recheck it, please, if it's 48.


OK.


OK, 108 squared.


is equal to 11,64, then minus


4 times 12 is 48.


times 182, is what? Is that correct? 182.


Yes.


Yeah, I got the answer is 2.


uh, in the radical,


underneath the radical is 29


I got this


+ or minus


radical.


But that square rooting it yet.


what


We're not square rooting it. We're, we're just prioritizing the inside of the bracket.


Yeah


Yeah, I know. Inside of the brac, well, I'm doing this. I don't know what you wanted, but then this is all over 24.


Mm


It's prioritize what's inside the


the boxing. Can you reconfirm the thing inside the bracket like for a square of 43.


Well, I did, I did this, this whole thing here


Oh


Oh.


that's equal 2928.


because this, this is square, right? You should have a, it's really minus 1.


What, what number did you get? 45?


not 45 it. It's still oh, I actually was wrong.


What


What the freak is


wrong with the calculator? Why is it giving me multiple


answers. I think.


OK, just give me uh 22 numbers here. So


this


yeah


It's officially 29


So we're both right. Oh my god, oh, I didn't see cause I didn't move. I only saw the 28, 0, OK, I see it now, great. We're gonna do the evil twin thing next.


y over to 4. We do this for positive.


OK


hm.


to


that's just


OK. Oh my God, this is the pains of having a oh my God.


But 8 over so.


Cancer can be. OK, I'm gonna do this, uh, fracture, 108 minus square root of square root of tuna to 8 over to 4.


Let's reconfirm is 2.2


and this


when you add this, it is a different number. It is 6.7.


I will redo it. The manual calculation.


Yeah


Well, OK, you got two answers here, right? It's plus or minus. So there's two, you're finding two zeros of this. Remember what we're doing.


We're finding the Max and Min points of this.


um


derivative


I have to think through


108 + 2928 and spirit of to


Then then until square root. OK, 2928 and we divide this one.


6.7. OK. This is boat right. Let's, let's continue. So since we have both of these, that's subject to this from the original number that we had. I'm not really urgent number, the original like I know.


OK, so I got just uh let's to clarify, I'm kinda um


I got these answers to be


the two answers are about


let's see, 6.


equals


Mhm


5. OK. And then I also had 4.5, that'd be about, it's about 2.


Oh, OK. And m is 6.75. I just wanna do it full bar.


I'm, I'm um


let's see, it's a little bit too.


very, but still, speaking of two decimals, OK, 2524. What we can do is that we can substitute this with the original formula with the formula, I'm gonna pull this up. The formula that we originally had uh for X-rays the part of 3.


Yeah


minus 3


Yeah, you could, yeah, you can do that. Let me show you, let me look at their solution a little more cause we're getting caught up in a lot of numbers.


Yes, we are.


Uh.


And uh there's, there's easier ways to do this, and I just want to see what they've taught you. Can you um


can you bring this, can you pull this sheet over here so I could see it a little more.


Mm


Oh, wait, where, where are you?


Are you going you up again.


Up to the original problem.


um,


I, I think I can move this.


OK


can you move it, move it to the left cause I, so I can see it. I, I wanna see what they're


OK, here. It's much enlarged right now.


OK, where did you put it? Down farther? I can't.


Yeah, it's much bigger.


It's


mm


You just subs substitution and then you just make the box of X and Y.


I don't, I don't see it. Let's see.


because they can always, uh


I still don't, I don't see the second sheet.


Oh


Can you just put it on top of the first sheet because I can


OK, OK. It's, oh my God, can you see it?


I


OK, now I see it. I see it. That's good, that's good. 00, move it back to the, OK, I can kinda


Yeah


that


s


yeah, move it left over the top of the other one, OK.


and


All right, use the quadratic.


So they call it a turning point. Yeah, I would, I'd call it.


maximum. OK, that's fine.


Well.


We solved the quadratic formula.


it's the box, the box is in the way now. OK.


That's OK. I, uh, no.


but on the way. We, this is how she


now.


I'm in. Here, I think you can see it better. There is no solution blocking it.


I sure, I, I still can't, I can't see it. I wish I could. Can you move it this way?


Do that. Let me just look at it a little bit.


Suitated. OK.


I don't know how we do it myself. OK.


the numbers.


Oh jeez


down. Wait.


what


Do you mind if we clear all the work we have now, we can just delete it or do you need to save this?


And you say there's no. Oh wait, no, I, we still need to do the substitution and I need to do the drafting, but


OK, OK. Um


um


like


Yes, times


All right, all right. Well, I guess you can, you can plug these numbers into this equation and get V of X, but let's do a little, let's get a little graph going, huh?


Yeah


Let's start. Let's get a little graph before you plug in these numbers.


OK


Now let's go down to the bottom.


Let, yeah, let's go down to the very bottom.


here.


of the grass


Let's go to the bottom of the page. I'm just gonna guess that they


I still need more. We're kind of running out of space. Do we have any more space?


but we are. OK. Uh, I can, I think I can make the


uh


Can you make a new page, or let's, let's


No, it's, it's down. It's very down.


Yeah, pretty new


Uh, you see, the thing that I'm drawing


ah


it's something


Oh yeah, here.


Let's let's um delete all this stuff, man, let's try to erase this, maybe, maybe this is what we need to.


do


Here.


Let's just erase this because this is just work. This is scrap work here.


No, this is kind of like the solution that our teachers finding. We can do like the, the thing down. You can do the thing down long. It starts.


OK, can you check, can you take the page lower? I can't see. I can't work. I got no spot to work.


Oh, is that


you can scroll it down, it's quite slower actually here.


Mm, really


Yeah, there's more, there's more space actually in the whiteboard if you, if you just scroll down.


OK


Yeah.


I tried to, what's this do? The 4 screen share, OK.


I.


Go back. OK. What's this?


If you, if you scroll down, there's infinitely more space.


Yeah, mine doesn't, mine doesn't seem to let me do it.


Oh, what device are you using? I'm just, I'm using, I'm using, I'm using a Chromebook right now.


Upload vote. Oh, I got a um


laptop


Yeah


Well, I don't know. I mean, I


I guess I could work it on a piece of paper and upload a photograph


OK, OK, OK


Uh, for the


yeah,


So I'm running out of I'm running out a little bit of time here. But let me, give me those, I'm gonna give, I'm gonna draw a picture and upload it in a paper in front of me, OK?


So can you give me the zeros that you have?


Uh


Uh, desserts that we have is just


uh 0.


There was one at 0. We, what, what was the other zero of the polynomial 6.5 and 7, right?


Yeah, 6 and 6.5 and 7 and 0 and 0. Wait, 0 and 0.


Now, this is only 30s, 20, 6.5, and 7.


And can you give me the uh what's the formula for VFX again?


Uh LWH land with height.


What?


Yeah, I know, no, I mean the, the V(X), we got, we got a polynomial up here. I'll scroll up. We, we calculated something.


This is, this is hard. I need a better way to


A woman


OK, V(X) is equal to 4 X cubed, right?


Yeah


minus


54 X.


square


4 y + 182.


Calculus X. OK.


So


um


at one


OK


Continue


uh


uh, we already have the X. I think the reason why they wanted us to substitute after was that we can make like the turning points for the Y.


let me


Yeah, yeah, I, I got, I'm giving you a picture here. Um


this point here is


OK, uh, let me speak from there. 6.75.


minus 54, 6.75 square. Yeah, I think 6175. For the first, the first turning point for X with the with the uh 6.75 for the first turning point, if, uh, for the 6.75.


Can you see what I've, oh wait, can you scroll up back up where you had your, I don't know, I can't change colors. The one where you had, you wrote in red the matching thingy. Why is it like this.


I


I see a but.


Shouldn't Geometry


Wait,


Now how are


How are you graft this.


God is so big.


OK, your maximum volume's got, OK, I'm gonna take


this


Oh


Let's see how, I don't know how exactly I'm gonna do this, but how do I say this is so difficult to work with.


Yeah.


If you do the substitution for the 6.75 is 1.6.


still 1.6


It could be a negative. I think if you put in a


from my graphs, if you put in 6.75, you should get a negative result.


Yes, that's right. I just forgot to mention the negative when I wrote it in the board, it is negative though.


And then when you put in 2.5, you get the maximum. That should be a positive number.


Wait, yeah, 2.2


Oh my God.


Uh, the Quran, it's a positive 181?


Yeah


and it's not that bad.


Yeah, that, that could be right.


I'm gonna


Can you


can


can you double check on my word, uh, when you sensitive it.


uh I'm gonna, well, OK, let me just, um, I'm uploading a photo. This is


I'm taking it on my phone and then I got a upload.


kind of a


OK


convoluted way of doing it, but I would try.


I'll try to get you a picture here.


Oh


cause I'm kind of learning how to use this interface. I've only been doing this tutoring thing for


Oh, did you realize in this interface, you can, if you have the mass, you, you have a mouse with you, right?


Yeah, I have a mouse. I also have a style that. What else can I do? I'm just learning this.


Oh, basically in this app, like in, you know the thing in between the miles from the left and the right, there's the whey thing, right? You, instead of scrolling like up and down, you kind of use it like uh MS paint where you just long press it and you can just move up and down.


You long wait


Well, I know how to do, I know how to move the cursor up and down. I can move the page up and down. I can't move it left, right.


Um, but here, I'm gonna try this now.


No, like, like what you can basically do is like the thing in between the scroll up, like the thing in between the left and the right, and I Lenovo like maspa right now what we can do is that, like you hear the song, like it clicks like.


your long press it and that's how you can like move up and down.


Are you long press it on your left mouse button? Oh, right now.


If you hear the click click


that's the sound when you realize that you can, you can move it.


Oh yeah, I got, I got a, I, I got a wheel. I can


I can do that. What I'd like to, I'd like to be able to draw better, but yeah, I can't. I got a stylist, but it's hard.


Um, yeah, uh.


All right, let me continue this


OK


Let me send you this picture and we can talk about it, OK? I think that's maybe, I think it's maybe my best.


way to do this


So


I'll send you the


Well


uh


come on.


when


and looking around.


and


Uh so.


go up in the player.


yeah.


and.


but it was a picture


Never mind.


I.


again.


Let me


see.


OK, let's see. I don't know if this is gonna, how this is gonna work, but


Oh, how are you gonna


I'm trying to, I'm trying to upload.


upload photos beside the band


Mm.


I'm trying to upload an image.


um, but I don't know, I've never tried this.


OK


Oh, you know where, where the button to upload this.


Do you see the image I uploaded sideways. I can't rotate it. Well.


Oh, I will, I'll, I'll rotate it. I have, I have been


Can you, can you rotate that?


yeah


I wanna just show you what we're


You did though.


yeah.


um


I want you to, I want to show you what we're doing before you


fact.


I'm gonna, I'm gonna rotate it myself.


Oh


I like to talk


or I could, yeah, there you go, there you go. How did, how did you do that? How do I do that?


You do the long press technique that I told you earlier, the thing in between where you make the really like when you push it really hard and, and the, and the screen like the, the, I'm gonna draw it for you. When this like.


when the


OK, I see it now. I can do it. All right, I got it. I got it. Trust it, you press it hard.


uh basically becomes like when it becomes like a grab handle thing like a glove.


that


Yeah, I just like Photoshop.


' s when you learn how to rotate it.


Oh, also, I also, I've been on this app for like for like once for like a semester already here.


I really needed free tutoring.


Yes, I'll, I'll continue out to then.


OK, can you keep rotating that for me. That will just, let me talk about, I'll talk about the answer and then I'm gonna sign off here.


OK, I'll continue roating this, um


OK


that.


So if you do a long press, you get new options is what you're saying.


Yes


Wait


OK, I found the green locator me


That's right. I got it. Here


I, oh my god.


I got it. I actually got it


Can you see it now?


I don't know. Let me try out.


I, I rotated it already.


I, I, I can't see it.


I can't sit.


I, you, you're looking at a different


spot than me. I don't know. I, I can't see what you're seeing.


Oh, try scrolling down. We find you.


OK, home messages, uh.


I you.


all right


OK


OK, well, if you can see it, if you can see it, I, I know what I put on there. So let me just talk to it, OK?


OK, OK.


Mm


OK, so you see what I, what, what is, what is this picture? What is this graph? What is the graph represent?


The graph is being represented by like, uh, it's, it's basically like a half W, the best, the best way I can describe is like a house.


Yeah, it's a, it's a, it's a polynomial of 3rd degree, OK? It's VFX. I've just grabbed the the YX is is Y(X).


OK. It's the volume as a function of X.


All right


Yeah


Now notice we found the 30s. You see the 30s of VFX.


Yes


They're at 0, they're at X equal to 0, X equal to 6.5 and X equal to 7.


Yeah, I can see it.


2.5 6.57.


It just runs a couple of you.


Yeah, this doesn't


It forms adult from that I've seen.


it basically forms a duct.


4.5 minus


W


OK, then, OK, so then,


uh those are the three 0s. Now, notice what 2.25 is where we took the derivative and we found out where the maximum was.


Yes, that's like the turning point where it rises.


Right, and you


and when you


this, it basically rises because if it's even if it rises. So we have like


and when you plugged in


uh like a table for that.


when you plugged in 2.25


to that polynomial. You said it was is that. I'll, I'll give you a number. Let me just finish, I'll do this, I'll check your number a little bit here.


I don't really like 2.25, but I'm gonna


let's see, let me pull my calculator up


OK, 2.54


I'm gonna put another decimal point on it that I want to do


I wanna


X to the 3.


OK.


OK, minus 54 times.


Yeah


2.254 squared.


plus 82 times


Oh we her a message AC.


Uh


Oh


Oh, I, I'm starting to get it now


I pray for protection.


The calamities


right


Is it m-54 or is it + 54


It's minus 54.


Yeah, signs 53


Yeah, I'm getting


oh, wait a minute


I


I'm looking and.


pass on the person.


was


both


huh


send you.


I'm just looking at my Google Classroom. There's spanning something one,


if you


what is this project?


me to


this, did you meet a table up and I'll do it myself.


I'll do it myself. OK. Can you please continue doing I know


the math


Yeah


Anyway, so that's the um


I am not quite


I'm not quite getting


I put in


one.


I called.


Mm.


There is no pa.


What the


hell.


You guysration. Can you continue, like what were you talking about you would


Yeah, yeah, I'm just trying to, I'm trying to check your, at 2.25, what did you get it should be?


uh 2.25 for me, like what I mentioned earlier, wait, let me go up. It was negative


1.08 and the other one k.


So you 0.5


For 2.5, it 1.5.


Yeah, it's like my graph is wrong.


Um


C


see.


Yeah


it's not correct. Uh.


yeah, some, something seems wrong.


Good, good today


Do you have the answer


I'm weird


huh


I am for, for, uh


2.5, it was 181 and 6.75 was -1.6.


Yeah, that, that would be, that sounds right, but I'm not able, are you


am I plugging into the wrong formula here? What do I got? Is that 4X


What's V of X? Let's make sure I got that right.


OK


Is it 4 x cubed?


The VLX like the formula that we bought.


Yeah, OK, it's the same, yeah. I don't know why, um


OK, it's the same, let's go. OK, so what we can do is that we just grab it.


Since it's a 10


Yeah, I did, I did draft it for you.


That should be right.


but there's a missing 108


Wait, what am I gonna wanna wait.


Do you have a graphing calculator?


I unfortunately do not. I just have the regular caso the, the 9 ADS, the FX 9 ADS. I don't.


Uh, if you're doing, if you're doing AP calculus, are you doing AP calculus? Is that what you said?


Yeah, I'm doing APL.


Well then you probably need the uh graphing calculator, don't you?


We, we just, we actually just


started and


I'm not really started, but this is my first time and like I actually did have a graphing calculator, but


I left it at school and I only have my backup calculator with me, the SCO one. But yeah, I will make, I will get my other girl. I'll get my other graphing calculators, so we can check for this. In the meantime, since there is online graphing calculators.


Sarah, yeah, there's a that was all my calculator. Let's see, let's see what we can do with this.


Yeah, online graphing calculator. Good idea, good idea. Very good idea.


For X-rays at 53.


Because I'm


94 and then they X-ray the power of 2.


and there we get a negative, oh my God.


OK.


see


I'm just, so when I plug into my calculator, I'm just not getting. My my uh


Oh, that's so cool. I'm right. It reached out.


It's 30


I wait


wait


I mean is the right formula or my speaking. Oh my God, you use 0, you use the wrong, uh no, you use the wrong formula for the graph. It's not 82, it's 182.


Oh, it's 182.


Ah,


Oops


Ah, it's, it's like a house shape


I


from using things that you might understand.


OK, it's 182. OK, that, that's probably that's why my numbers were wrong, right. So change my pic


Also think


Everything else about the graph is right except the coefficient.


So if you put in 4 X.


yeah, it's one, it's that so


cool.


It was very 2.24 181, which is really, oh wait, what did I, what did I write? Wait, I made a mistake, but this is somethingsomethingmething, so which means that I was really close, so at least we can round up the 1 to the 0 and we.


Well, remember, remember, you didn't have the, their, the actual 0 is like 2.254.


huh


So


2.254. 0 yeah, it is, it is.


yeah, yeah, you gotta go back to the quadratic. It wasn't exactly 2.5.


2. It was, it was 2.254, not 2.25, you know, it was a.


Yeah, I'm sorry. Yeah, but at least the difference is that


oh, yeah, it that doesn't excuse it. 2, but like


it still is this


actually


I was mistaken. 180


181, 2.25


the decimals actually had


2.245. It's reversed like, let me check. OK.


I


uh.


Oh


what this my nose? what?.


don't, don't know the area. I know


so he always 24.


So, uh, 2.2. 0, we rigged it wrong. Oh my god, they did it wrong.


No, we didn't


Oh.


I think


I'm so blind.


I think uh you got pretty good answer. What's, what's the problem?


OK, we actually did it, oh my god, we did


it, OK, I'm free. Thank you.


Thank you


Yeah, you got the right answer. That's right. The only thing, if you look at my my picture, um,


Yeah.


it should not be 82. See, I was trying to plug into my


equation that was wrong. It Pre-Calculus. I didn't, I didn't copy the one, OK, because I can't really everything's, I can't really see stuff. It's hard to see.


Mm


But you got all the, you, you understand what we did there.


Yeah. Oh my God. I hope I can favorite you as a teacher so that we have more probabilities of meeting again cause this is our final project, but we still hadn't had our finals yet and basically what we've covered is basically long division of polynomials for like calculus itself.


for long division of polynomials. We had synthetic and then uh going closer to the graphing of the actual graph itself was actually like


uh


uh finding all rational routes, finding rational routes and the kind of the rational root theorem and then the last thing we did was graphing, which correlates to our final project, but actually the thing is our teacher never actually thought us about derivatives until our final project, so, uh, I just saw it on a video because we were, they just sent it as a video.


They never actually thought us after to they never taught us face to face cause


it


Uh, so you never, you never learned the product rule. Yeah, you need to learn, you need to, in order to take derivatives, there's a whole bunch of rules you gotta learn, so


Oh


she


But anyway, let me just remind, yeah, so I just gave you, that was a simplest derivative rule was the one I gave you. The, that was called the Power world.


Oh, yeah, that's easier.


Yes.


Very good. OK.


Now, so what did we find out? What, what, what, uh, if you wanna maximize the volume in the box.


What do you


What? OK, you wanna maximize the volume in the box.


have


Where do you find it? We, we, we, I thought we


saw it


We did, we did, we did. I just want to know what value of X and what value of X does the box volume get maximized?


Why is it turning? Wait, let me


the grass


the graph where the circum.


So I'm I'm asking you to interpret. I'm asking you to interpret what the graph means now.


OK.


OK


You're, you're trying to remember what we're trying to do? You're making


6.5, 5.


um


Yeah


hold on a sec. um


you're trying to maximize the.


Actually, I think it made kind of a mistake with


No, there's no mistake. I think we got it. I just want you to understand what you did.


2 divided by 24.


No


Now, you see the graph.


Oh wait


wait, 6.6.7.


6.75. 0 yeah, 108. I was right. I, I mean one.


I probably wrote this 1 1.68 but then I thought the 6 was a 00 my god, I guess.


up.


A uh Uh *****, I got a


I gotta go here. I just, my last thing was uh


Thank you so much for this though.


um, listen, if you look at the graph, you see how the, the graph is at its maximum at what when X is equal to 2.54.


Yeah


So when, when X, when you make a fold in the box of access 2.254 inches.


Oh, she, she.


You, you're actually maximizing the volume of the box.


OK


Oh, OK. Oh, OK. Thank you so much for this and for


OK. All right. Have a good day. Have a good day.


Bye-bye


Thank you. Have a good day too. OK. Bye-bye.


Hello How are you?


I am doing fine, thanks


How can I help?


I need help with unit 1.5 Of precalc sort of confused


I do no tknow th eunit numbers but I can help


Alright, the unit is polynomials


could I send you a photo? would that help?


Do u have specifci questions?


Yes


How do I do that


OK You should see an icon that


looks like a mountain and a sun with an up arrow


Ah got it, thanks


ok


OK I see


it


Great!


I will copy to 2nd sreen pls wait


got it


OK What questions can I hep with?


OK


I just dont undertand the concept


understand


do u know the deifntions for even odd and "none"?


for Alex


Yeah if f(-x)=-f(x) it is odd if it f(-x)=f(x) it is even I forgot how to input that


OK good


Now look at 1 a)


if you replace x by -x then what happens?


you would multiply it by the fourth power and it would become even?


sorry


postive


OK yes


let us nack up


1 a) has only even powers do u agree?


Yeah, because when you input the negative the outcome is positive?


Yes


for example 3^2 = 9 and so does (-3)^2


Yeah


And that works for all the terms in 1 a) I guess we could write the 5 as 5*x^0


OK?


yes


Also IF you grpah the function


it whould have a "mirror image" across the y axis


Oh. That makes sense


Now in 1 b)


the powers 3 and 1 are odd BUT I think the  -1 means we have "none"


or "neither"


well why would it be none


OK I will check but here is what I think


for x^3 id we change to -x we change the sign do u garee?


if*


and for x^1 also but I htink we can think of the -1 as -1*x^0


and that does not change see what I mean?


Oh yeah I can sort of undertand that


OK good


do you use Sarah and/or a habdheld cacluator gor grpahing?


handheld*


I dont have a graphing calc, I do have demos tho


OK well after we are done try grpahing 1b) and then remove the -1 and grpah it agian


I have onle 15 more minutes,


so do that later OK?


Ok


now in 1 c) we have a grpah


Is there also an equation?


No my teacher  didnt provide one


OK I see


well do you notice that in 1 c)  the graph is sort of "reflected" thru the origin on each side of th y-axis?


1,-3 and, -1,3


let me think


yes


1 -> -3


now if we change 1 to -1  -1 -> 3


so f(-x) = -f(x)


Ohh


so that type of symmetry in a grpah indicates an odd function


excuse my poor typing


I falied a typing class a long time becuase I was bsuy trying to take aprt the typewriter


No worries, I understand that, I sucked at middle school typing


OK


Now in 1 d) I see no symmetry


so what do u htink abotu 1 d)?


well there are no points that are really like inverse to each other so it cant be odd


and  its not exactly like similar to eachother


I agree


so I doubt its even


Yes it is neither


and I added some confetti !


Lol!


OK Now suppose we shifted the entire 1 d) grpah left by one unit (on the x -axis) what Alex think that would do?


it would be symmetrical


Yes


so it would be even than


then


Yes I agree


yay


More confetti LOL


I have about ten more minutes


idk if its possible but could we go over 1 more thing


alright


OK I will copy


pls wait


sounds good


Got it now I will read it


got it


OK I was taught to think of domain as the entryway


becasue it is the nubmer that can go *in* i.e. the allowed x vales


So what do you think the domin is for this funcion?


so like infinity to- infinity?


tho I would put the - first


ohhhh yeah


-infinity-inifity


I ment to use the one in the middle as a coma srry


OK


I got it


Now how about the zeros?


bcuz y is 0 there


ok and their multiplicities?


I think the first 1 is 1 and 2nd is 1 and 2 is 2


could be wrong


I agre with you


awesome


and d)?


-4,-2 and 1, infiity


I agree


but the -4 looks like -4.1 but my eyes are not so good


How about decreasaes?


oh yeah, id say -infinity ,-3.5, -2,1


but the 1 lloks like .9 ot my eyes


Alas, I msut go now


yeah I think It is


aw thanks so much


You seem to be getting this materail now


I hope this helped


yeah I needed to look over it again, thanks!


OK and try some gaphs in Sam if you have time


ty i will


OK Bye for now


bye!


hello, how are you doing today?


Hello, I am doing great, how are you? I have 10 questions to ask today on a doc I would like to screenshare. Is that okay?


that would be fine


alright, I just resized the screenshare


im not allowed to use a graphing calculator so I am having a hard time with tan, sec, sin ext


oh alright


real quick, can you show me tan, cot, sec, and csc in forms of cosine and sine


I think I gave confusing instructions


for example, tanx is sinx/cosx


oh


thats kinda the way that I want those functions


Sorry trig is confusing for me


thats fine, its probably the most annoying part in calculus


ah one second


i see how you got 1 over cosine


but cscx is actually 1/sinx


the co things is kinda confusing


great!


now how much do you know about the unit circle?


not much, im pretty bad at it


thats fine


so ill just draw it rq


a trick that we can use is that we only need to memorize the first quadrant


and then flip the sin and cos values based on the theta values that are given


so do you know the values in the first quadrant?


not quite


so ill write them out for you


so when getting sin and cos


think sin as y value


and cos as x value


those are the values of theta


so if you put cos(ppi/6)


you would get sqrt(3)/2


and if you put sin(pi/6) you would get .5


sorry i just couldnt tell what values were under pi


so another thing you can use is that cos and sin will either be sqrt(3)/2 or 1/2 as long as the denominator is not 4


oh ok


thank you sorry


no worries, if something isnt clear feel free to tell me


if the denominator is 4 for the theta value, then the value of sin and cos will either be -sqty(2)/2 or sqrt(2)/2


an example would be theta = 5pi/4


or this line


what we can do to think about the sin and cos values would be flipping the line theta = pi/4 over the y axis


then flip it again over the x axis


if you flip over the x axis, you multiply the y value by -1


and if you flip over the y axis, you multiply the x value by -1


does that kind of make sense


yes


great!


now once we get our sin and/or cos value, we can plug them into the other trig functons


so how about you try question 50?


ok


how are you doing so far with this question?


oh sorry i didnt see you work down there


alright, so not quite


do you remember what happens if we raise something to the power of 0?


it turns into 0


o wait 1


yeaa


also, is tanx = (cosx/sinx)?


no.... :( sin(x)/cos(x)


lets go back to the unit circle rq


can you use a colored line to show where theta= 0 is


nicee


so what would the cos value be?


yup


now if cos 0 is 1, what is sin0


so using that, what would sec0 be and what would tan0 be


tan0 is correct


but lets check sec again


what is secx?


now what would we get if we put in 0 for secx


so what is our final answeR>


answer?*


nice!


do you want to try 49?


yes please


i will take a second


looks right to me


is it fine if I erase the board?


Yes


great


now lets move onto 52


let me work it out myself then ill get back to you


ok


sorry for the wait


that totally ok


did you try while i was solving it?


*is


kinda


alright


so I did this in a more complex way than needed, but I think I know the easier way


so what was your first step?


my teacher said it was wrong


said what was wrong?


and after that i had no idea what to do


my answer to this question


ah


its an old test im looking over


well it would help to see exactly where you got it wrong so that we can fix that error


here I can upload it onto my screen really quick


its on there, but I can't rotate it


i see the question, but II dont see your work


ah i see


you put in 2 instead of a


since the limit was where x goes to a


also with substitution, you got 0/0 which is an indeterminate form


the pencil is me and the blue -2 and slash mark are from my teachers


*teacher


good to know


I do see that you subbed in 2 for x though


oh sorry


thats how my As look


sorry


i read your a as 2


myf


no i just read it wrong


not ur mistake


so the problem here is that when subbing in a, we get an inderminate form


that means that we need to do some algebra to get our answer


how can we simplify the denominator?


oh... i guess i just gave up and said 0


cross the a's out


well these types of limits are the harder ones so no worries


well we cant quite cross out a


since we are subtracting a in the top and adding a in the bottom


if they were both subtracting or both adding we could cancel both of those terms entirely


but we cant do that here


instead, why dont we multiply the denominator and numerator by (x+a)/(x-a)


that would get rid of the denominator completely


yup!


now we can do one more thing to make our work easier


foil?


thats one method


but not quite fiol


its more like distribution


since its just one big term


but we can do this another way to avoid messy work


do you think you can see it?


if not just tell me, its all fine


yes


not quite


what I saw is that we can combine x/a and -1 into one fraction


do you think that could be useful for our expression?


great! show me how this could be sued


used*


yea!!!


well


dont forget about the a at the bottom


nice!


now one more thing


what are we missing on our expression?


oh we cant cancel out our a


the reason being is that the term on the top is x + a and at the bottom it is a


there is no factor of a on both bottom and top


so nothing is cancelable


but we are missing something important


hint: look at the left of the expression in the original expression


a negative


not really


its a shortened version of an english words


word*


can you see what i wrote in orange a little lowr?


oh i see it now


yea thats right!


so what would that be?


isnt that all I have to do?


well we have to find the actual value


since its asking for the limit


do I just make up a number


or put 0?


well no, we can use substitution here


with the a?


reason being is that when we plug in a, we dont get an indeterminate form


yes


but wouldn't it be the same.


wdym


ohhh! pput the a into the x


yea


u got it!


since we subbed in a for x, we no longer need the limit notation


also what is 2a/a simplified?


yeaa


so our final answer would be 2


can I write this down super quick


write what down?


oh just onto a notebook so I don't forget


oh yea


go for it


I can do one more question and then I will have to leave btw


could we do 19 then?


i put it at the top


sure


can i eras the whiteboard?


yes please


great


let me write down g(x) rq


i got the reduced form, but not the other parts


alright


so ill just simplify rq


so where does the y intercept occur?


when x=0


great!


so how can we find the y intercept using this knowledge?


do we plug it into the orginal form?


0 for x i mean


yup, but its best to plug it into the reduced form


so what is our y-intercept?


yup!


so what is that as a coordinate?


there you go!


now lets move onto x intercepts


where are x intercepts?


when y=0


nice!


or in other words g(x)=0 right?


yes


so do you think you can find where the x intercepts are?


yes, one second


of course


do we only want the numerator?


to equal zero?


yea


can you tell me why though


because if it turns out to be a zero everything doesn't blow up?


yup


or since you multiply the denominator to 0


so what are the x intercepts as coordinates?


or (1,0), (1,0), (1,0)


and (2/3,0)


can you show me how you got that?


one second let me put it on the shared screen


alright


rq can you confirm if the expression i wrote at the top is correct before reducing


where?


i circled it on the whiteboard


looks right to me


its what I have on my paper


then I believe you reduced something wrong


since we have different expressions


for solving for x intercepts


was I supposed to take the numerator of the reduced form?


numerator of reduced form


you onyl put each point once btw


oh.... I took it from the orginial


you are right that the multiplicity of the point is greater than 1 tho


but it wasnt asking for that in the question


is it just (2/3,0)


yup


and one more


nice!!


is that all in that question?


I also need to find the HA


ah ok


so end behaviours


so we would need to use the reduced form


as otherwise we would be dealing with holes


are the all odd


move to the top of the whiteboard please


wdym by odd


nevermind


alright


so what we do here is expand our denominator and numerator


do you think you can find the HA from here?


is it 3


yup


from the ratio of coeff


correct!


is that all for this question?


yes! thank you so much!!


bye


np


have a great day/night!!


you too


Hi Jamie


Hi


I just need to go over points of concurrency


sure


I understand it but I just want to go over for a test tomorrow


do you have a problem to work on?


Yeah let me put it on the whiteboard


ok


How do you memorize the terms


that's a hard one


for circumcenter, I will circle


My teacher had a phrase he said


okay


what's the phrase


I forgot


no problme


it is rather intuitive


circumcenter


must be related to a circle


Oh wait all of my children are bringing in peanut butter cookies


oh I see


how is this related to all the points of concurrencies


Let me put it on the whiteboard


I see


I think this makes things unnecessarily complicated


centroid --> mid point


Orthocenter --> Perpendicular


circumcenter --> circle


Yeah my teacher said it and I was still confused but I understand it


I was confused on memorizing it


So the circumcenter is


I don't think you should try to remember this


Yeah I think your right


do you want to work on these 3 problems now?


Sure


oka


okay.


Circumcenter is perpendicular bisect or


So like the midpoint and slope of the line


yes!


So I’ll just solve it out first then


let's find the equation for two perpendicular bisectors


Okay


So I’ll write it out?


you can work on a piece of paper, we can then compare numbers


Yeah sure


Sorry I just started


no problem. I am also kind of slow


Wait I think I did it wrong


I got 14 for x


is it possible for x to be that big?


the maximum of x is 6 for the 3 vertices


I did this in class with someone else and got it right


let me work on the board


to make sure


I know the answer was def not 14


exactly


let me graph it so you can get a sense on what x can be


I will work on the algebra on the board


does this make sense?


I got the same slope but for the mid point I got (2,3)


Let me check


ok


Yeah it makes sense


let's continue


Yeah


I used the point-slope form


Yeah same


That’s how my teacher taught it


great


next, let's do AC?


I did cb


no problem. I will be cb as well


Oh yeah I got the slope wrong


I see


it is very easy to make a mistake


Wait is it suppose to be positive


you are right!!!


so the slope for the perp bisector will be -2


how do you solve this system of equations?


You simpfly it and make it equal to each other


yes!


we can also subtract one from the other to get rid of y


Oh yeah


this is what I got


Let me solve it out


ok


Do you have to distribute?


I did


Yeah it is 19/7


great


now you can compute y


Idk why it’s not letting me write


Oh nvm


that's what I got as well


so it should be right.


Yeah i have the answer key


cool


you want to work on the 2nd one?


Yeah


ok. let's work on paper first


and then compare numbers


Sure


I got x right


great. y is relatively easy


once x is correct.


Oh yeah


yes


you are good!


for the centroid, there is actually a simple formula


Omg really


I will use that to check my work


yes please


thank you so much :)


you are very welcome.


I actually have to drop, but I think you are in great shape.


Okay thank you so much


bye


Bye


Hi Ben


hey, again


Hey sorry abt last time


It was just last minute


and i had to do a couple things


what happened last time?


I had to go bc my mom was coming


remember?


oh


i got to go sorry my moms coming
byee


yeah


no problem


hey i had a question


moms have priority over tutors


what's your question?


is it about holy water?


no lol


if student could favorite coaches, can coaches favorite students?


no.


but I maintain my own spreadsheet of all the kids I tutor.


They get a checkmark or an X


that's cool


oh did i get and X


I don't pick up the session if I see an X by their name


I'm here, aren't I?


oh ok yay


I think i favotited you


students who tell me jokes usually get checkmarks


lol


favoriting doesn't do much of anything


oh the bot says you get them if you favorite them


but i guess it lied


when you request a coach, every coach certified in your requested subject still sees your request as soon as you make it


coaches who have set up available time intervals get text notifications when a request comes in.


I have a question, do you know any other coaches?


they get those texts a few minutes before coaches who aren't favorited


or are you not allowed to tell me


oh oki


I've had conversations with some other coaches. we have a slack website with different topics of interest to coaches.


oh ok :)


but I've never met any of them and don't really know any of them.


have you talked to any of them?


no


just text conversations via slack


oh ok


and not many of those


oh


lots of new coaches go to the Introductions channel in slack and talk about how excited they are to join our community/team. Looking forward to working with us.


We don't really work together. We work with the students.


oh is there a chance that some of them go back to school and aren't coaches anymore


If a coach goes to the Math channel with a problem he/she can't solve, I'll often offer assistance.


Most of the coaches seem to be students. I think a lot of them sign up, then lose interest pretty quickly.


oh so they just quit?


they just stop logging in, I guess.


there's no real quitting process


it's not like we're paid or anything


i was jus gonna say that


we're all just volunteers


yeah u do it bc u want to


right?


we tutor when we want to


yeah, or because it is court ordered


(just kidding)


bro i thought it was a punnishment or somthing


a lot of kids tutor to get volunteer hours for school


I don't care about the hours


oh that makes you awesome!


I've got almost 1214 hours


wow sounds like my Xp in duolingo


in almost 4 years


oh


4 YEARS!


thats a lot of time


yeah. probably 4 years in December


I'm one of the oldest coaches here, in more ways than one


Thats pretty cool


yeah


I'm just here to help kids like you


need math help?


Do you know any famous old people?


no


lol


I've seen a few


so cool


ive never met a famous person in my life


was a few feet away from Oprah Winfrey


Om goodness


thats cool


Being rich comes at a cost tho


bc if your rich ur famous


being famous means not being able to go anywhere without being bothered


so thats why i think poor life is pretty good


you can afford the things you need and you dont get botherd 24/7


listen to the song "If I Were a Rich Man"


why?


is it a country song?


oh good


i dont like country songs


song from Tevye on the Roof about wanting to be rich


why would someone want to be rich


nevermind


i know why


it has its advantages


want to do math?


but it also has disadvantages


not really


LOL


that's why I'm here


ive done a lot of math since 5:00


sorry yeah one question


ok


i will put it on the board


hey before we start


do you know anything about being a doctor


no


i will listen to the song "If I Were a Rich Man"


but you have to watch a video if you have a tv


watch a video to see Tevye dance while singing it


what?


the character who sings it is named Tevye


oh ok


and he dances while singing


wow


Fiddler on the Roof is my favorite musical


cool


So you use youtube/


some, not much


math?


Watch a video by Sal Khan


yes math now lol


ok the problem says solve for x


pretty easy


I just marked 2 angles


what can you tell me about them?


ok first can i guess that x = 62 degrees?


no


oh man


well, you can, but it's wrong


oh


what about those 2 angles?


are they vertical angles?


when I grew up, those were called opposite angles, because they were opposite each other where 2 lines cross. name makes more sense.


now they call them vertical angles


do you know anything about vertical angles?


bro are you Geometry or something?


much earlier than that


lol


oki


let's just say I'Westwood High School reunion


my birthday is in 9 days


but im not that excited


what can you tell me about vertical angles?


anyway


yeah um nothing


cause idk abt them


they are congruent


what does that mean to you?


o yea


um they intersect


no


congruent means same


measures are equal


oh yeah


vertical angles are the angles formed by two intersecting lines (they basically point at each other!)


write an equation that says that


oh


um


ok


idk one


you have two angles


you have an expression for each one


and they equal each other


say that in an equation


wait can you gimme a sec ill be right back


ok im back


OK


equation?


oh yeah that


thing on left equals thing on right?


oh we are talking about congruent?


uh, yeah. vertical angles and all


oh i though we were talking about what i said lol


how about that equation?


do we have to divide 3 by x


pretty simple, eh?


kinda


we have to get rid of everything that is not x on the left side, starting with 2


ok


no


do you know the steps in solving an equation?


if there were parenthesis we would solve those first which is kinda what we are doin


this is not about PEMDAS


oh


sorry


solving an equation means isolating the variable (which is x here) on one side of the = sign


which means getting rid of everything that is not x so that only x is left


here we start with 2


2 is added to 3x, right?


yeah so 5x?


no, you can't combine them


so 2x3x?


jk


to "get rid of" something you always do the opposite math operation, and do it to both sides


what is the opposite of adding


so you subtract 2 from 62?


you subtract 2 from both sides


yes! so it cancels out the two!


write the next line


yes! opposite operations always cancel


3 is multiplied times x. what opposite operation will cancel 3?


now do we divide 3 by x


yes


draw a line through the 3's. that's the most fun part of this.


like I did with the 2's above it


good


all you have left now is x


and x=20


your math teacher (mom) should have taught you this


oh


she not really our teacher


we don't have math class


thats why we use upchive to do one question and learn from it


doesn't sound like a good method to make sure you learn what you need about math to me


i know


Do you know what TCTC is?


no


its like a trade school


home trade school?


we were supposed to go but she keeps avoiding it


it's not at home its public


we agreed to do half year homeschool and half year TCTC


but everytime i bring it up she changes the subject


isn't Freshman a bit young for trade school. Harmony High


what do you mean 9th grade


im in Sophomore


about the session says you are in Junior


check your profile


cause that's what the platform is telling me


oh its probably my mom


she created my account


she doesn't want you to grow up


and she wants to put me in a lower math grade


and once your grade is entered, it increases by 1 every year


she wants me to be "the doctor of the family"


you'Harvard University, then go to medical school


I don't want to sound rude but she wants me to choose the career she has always wanted


that's not for her to decide


ik


you have to live your own life


Public School education, she should put you back in school


I have wanted to be a police officer for almost 7 years now


i just cant imagine myself as a doctor


It just doesn't fit in place for me


you won't be happy as a doctor if you want to be a police officer


i know


she says that its dangerous to be a police officer


it is


I wouldn't want to be one


i think she is just looking out for me


I wouldn't' want my daughter to be one


and i appreciate it


and would try to talk her out of it


but wouldn't make her do something else if I failed to convince her


After my dad heard that i wanted to be a police officer he started watching these videos about currupt cops


doctor is a much, much better career, but a much harder path to get there


and now he just makes fun of me


he is always sayin how when i become a cop that im going to pull over my brother and arrest him for stupid things


he just doesn't understand


im sorry


for putting all this on your shoulder


but thanks for the advice


good luck dealing with your parents


I like to think my dad dosen't make fun of me i just think he doesn't want me to be like those people and he wants me to know the amendments


and follow the law


there are corrupt cops, but they make up a very small percentage of cops, in general.


every officer that my mother has told i wanted to be a cop they always say how they can see that in me


I have just always looked up to cop i just think they are cool


i mean most of them of course


*cops


I've got to go. I wish you luck.


byee thanks for everything


don't worry, you still have a checkmark


thanks nice talking to you


same


bye


hi


Do you prefer typing or speech


either is OK


ok


Can we talk then?


I just find it faster


Hello


Alright, yeah, go ahead. Uh, can you hear me now?


Oh yeah, I, I forgot to, uh, unmute, I think.


Yeah, no worries. Uh, do you want to share the questions on the screen and uh we can go from there.


Yeah, um, I had tutor before, but she didn't really get it.


like


it's, we have like a really weird


way our school makes us do math, I guess.


But


So if it's a messy, but I mean, they were writing really quickly, to be honest.


Which one are you doing? Are we doing the first one?


Um


or that's the only one


first one or second one, either one that you've like they're the same concept, but


it's like I just don't really get what's what I'm looking at.


or like how to do this or like replicate it by myself.


Where is the second one, sorry? Why is the


product ACX. oh, that one, OK, got it.


Me either one. I have a screenshots of both if you want the other one.


OK OK.


No, that's fine. Um, so let's, how do you want me to help you, like, uh, do you want me to walk you through how they solve this?


Uh, I mean


basically, like, yeah, I, I just don't really get like why they did some of the things


and just title like


did I like cut off for a second?


or


OK.


No, no, you're good. I'm just trying to uh


for this


Yeah.


on a page, so.


I'm just kinda


so this is about factorize. This is about factorization, right?


Yeah


Yeah, so simple method here is


mhm


No, but like they don't want us to use the quadratics. That's the thing. They want us to do it like the way that it's written there, and that's the problem. Like I've, like I, when I, I had to search up like the answer online because I just wasn't getting getting how to do it, but then I saw that they were using the quadratic or, I think that's what it is, right?


And


yeah, and like


they just look super different from what we were doing in class, and they were like, oh, you have to use the table and this and that. I was like, what?


There are two approaches to it. One is to find uh using the


equation, right, where you're able to identify the value of uh X with the formula minus B+ or minus square root or b^2 and 40 see that one, right?


Do you know that


Hm.


Have you, have you guys been taught that?


What, like the


standard for


The formula to find the value of X.


Uh


OK. All right, let me.


not necessarily. Like I don't really know if we have or not at this point, like, like formula, do you mean sorry?


OK.


let me go through this first one and then I'll, I can show you the alternate one also. So, uh, and stop me if there's not what you're looking for.


So do you see the reion on the board already? That's typed in.


I, I wrote, rewrote the equation basically.


here.


Mhm


OK


Um, so this is the solids factorization, right? So you essentially are trying to break this down into two factors and make it a multiplication.


Correct?


Uh, yeah, I think so cause that's at least what I think they maybe does do.


Yeah, yeah


So that's the idea here. Um, so whenever you see this, you can ignore the first portion of it, which is this section that I just typed. Do you see 3 X square and I type?


So you ignore that and then you think about how do I break this?


12 down as a multiplication.


so that


But, so, uh, hold on, like,


are you saying like we're just gonna ignore the 3X square for a little while or


cause like, are you saying like should we just find the factors of C?


So


yeah, yeah, yeah. So we just hold, hold off on that.


Um, the first portion.


um, may you want me to like just start listing factors and stuff or?


I


No, no, so, but the idea is that how does this become a sum?


such that the product


is 12


You see what I'm saying


Uh, not really. Um


wait, so that bee becomes the sun so that the


product is 12 or?


Yeah


exactly


uh


oh, so then that would just be 2 and 18, no?


Yeah.


Right. Actually, no


No, so 43 is 12.


Uh, hold on, something's off here.


Uh oh


Cause there's like two X values though, so.


I mean.


like there's no way to just find like


one value of X, I don't think.


Yeah, yeah


No, there are two values that actually you need to find, but I am trying to figure out the best way to do this. It's like 12, 3:36.


36, uh


is 20. When X?


Um


It's like


hm


hold on, let, OK, before we jump into this, let me maybe, do you know the basic way of doing this? So for example,


X + uh


you know this method, right? So 3 to 6. So if I say X


right


were you writing that?


plus 6, you see this?


Uh, oh yeah, no I see it's OK.


not really.


So do you know how to solve this? Like, let me just type it properly, yeah. Do you notice all this


Uh


How to factorize this. So this is all like this, so you do X to the part 2.


then you do + 3X minus 2 X.


and then


the multiplication of


+ 3


multiplied by -2.


Let me put a dot so that it doesn't seem like two multiplications. You see this now?


Mhm


So what is happening is 3 multi blood by 22 is -6, and 33 x minus 2 x is X.


Me what? Wait, hold on. OK, so


OK, but then what was the point of that one.


Alex goes off


Oh, sorry. So what I'm saying is that you break this down, the X in such a way that 3x minus 2 X gives you the X, correct?


We found the factors of 6, such that the addition gives you the coefficient for the X and the multiplication gives you uh the coefficient, the


the


the last C number basically.


right? So when you do this, you are able to break this into two factors, which is


X.


multiplied by


Oh, so you're doing like the 2 is in common, right?


X + 3. Correct, yeah, yeah, you're right.


OK.


And then you take the -2 out.


and then you'll get the X + 3 inside.


So then you have two factors, X minus 2 and X + 3. So X is equal to 2 or X is equal to -3. Does that make sense?


No, I got a second.


uh


um, but.


um


not


Did you, did you understand that or, or slow down.


no, sorry.


OK


So what is happening here? Um, so because I'm, I'm sharing this because this should will make the other one easier for you. That's why I'm trying to break down here, OK? And then we'll go to that one.


Uh


so do, should I write the next step then?


Um, could you like explain


Are, are you on the same page to? I'm sorry, go ahead.


could you explain like the third line, like


pretty much


The third line? OK, sure, yeah, the third line, right? So what we're doing is


let me add a new line, so maybe that's easier than, you know, X is X, correct?


Mhm.


So what I did here is, if you multiply these two axes, you'll get the X X and X, right?


The same thing as that


Mhm


with me


Mm


And I'm putting dots. That doesn't mean it's decimal, it's just multiplication.


Yeah


OK. So this is X and if you multiply this 3 with that X, you get 3 X, correct?


Uh, yeah, but like


aren't you doing X basically times


X cause where does the other X go?


Which one, sorry? Are you, are you pointing to this?


Like


is there like a pointer on this, like you can see.


Yeah, yeah, I can see, I can see your name on the pointer.


OK, OK. So, I know like this is X times X.


but I don't know like how this is


broken up. Like I know like this, basically.


these two


convert into


Oh, this means 3 daughters. Do you know that?


Yeah, I know, I don't means that 3 times X, but


Correct, correct


uh, like


why does it go to X + 3.


or


OK, let me show it. So it's 33 x, right? Let me write it. Correct?


Oh, wait, wait, wait, no, no, no, yeah, I, I see that like it's cause I mean if you just think about it, you can, it, this just becomes X^2 + 3 x, if you think about it, yeah, yeah.


Correct. Correct, correct. Exactly, you got it.


And the same where I now, now I know one factor is explicitly already, right? Because that's what I got.


Mhm


So essentially, you need to make sure how do you get the other one is X + 3. So if you take -2 out as common.


then you see this is minus to X and this is


-6 + 3 minus 2.


Oops


I got something


OK. And I like consistently do this without like, like I know how to work back from the last form, but I don't know how to work to it exactly. Or at least not like quickly.


All right, so we go there, that's the next step, that's the next step.


Uh, so way of doing this is, do you know factorization of numbers like you, how do you do this? So let me just try it and, and then you can tell me. So this is 6


correct?