Datasets:
NationalTutoringObservatory
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MathEd-PII

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volunteer
Does that make sense
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student
Do you have an example? sorry.
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volunteer
Oh yeah, that's fine. Um
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volunteer
OK, yeah, I can show you an example, one sec.
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volunteer
I can just like do it below.
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student
OK
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student
I'll write it down also.
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volunteer
OK, um, wait.
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volunteer
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.
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volunteer
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.
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student
Oh, OK, OK.
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volunteer
Yeah. So it would be
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volunteer
um A is less than 0. And then a stretch is
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volunteer
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
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volunteer
you know, extra stretch closer to the axis.
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volunteer
Um, and that's called a vertical stretch.
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volunteer
So if it's a stretch, it would be a greater than 0.
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volunteer
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?
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student
A little, yeah.
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volunteer
Yeah, um
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volunteer
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.
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volunteer
OK, and then a compression is basically the number has to be between 0 and 1. So it
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volunteer
um, a compression is when it moves farther from the Y-axis. So like you can see it becomes wider.
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volunteer
So basically, if the numbers like
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volunteer
between 0 and 1, it would become wider.
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volunteer
Does that make sense
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student
Yeah, I get it.
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volunteer
OK
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volunteer
Yeah. Um
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volunteer
so
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volunteer
do you just wanna do the example, or if you have any questions, you can ask that.
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student
Yeah
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volunteer
Um
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student
I have
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volunteer
yeah, what were you saying
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student
is it
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student
um
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student
you and I, so I cut the screenshot doesn't show like the other half, but I have the other screenshot.
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volunteer
OK. Yeah, that's fine. Maybe you can just put like the other screenshot.
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student
OK
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volunteer
OK
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volunteer
OK. So for the first one,
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volunteer
Y equals -x squared. So how do you think the parabola would look?
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student
Um
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student
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.
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student
like a 1x and then square.
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volunteer
Yeah, yeah, it would be Y equals -1 x squared.
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volunteer
So like on the graph,
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volunteer
um,
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volunteer
like, how do you think the parabola would look on the graph.
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student
like plotting
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volunteer
Yeah.
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student
Uh, I think you start by, you start by, uh, 0.
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volunteer
Yeah
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student
underground
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volunteer
Um
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student
and then
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student
and then you moved.
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student
you move one.
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student
down like to the left.
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volunteer
yeah
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volunteer
OK. Yeah, so, um, to graph it, we can just like
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volunteer
uh start
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volunteer
um plotting like the points. So,
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volunteer
um we can start with X equals 0.
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volunteer
So if X equals 0, what would Y be?
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student
-1
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volunteer
Um
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volunteer
so X equals 0, we can just like
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volunteer
um if we have like the X value and we wanna see what why is. You can just plug it in.
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volunteer
So it would be like
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volunteer
we just plug the 0 in instead of an X. So,
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volunteer
um 0 times anything is 0.
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volunteer
So, basically,
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volunteer
if we did hear 0 times 0, it would just be 0 and then 0 times -1 would also be easier.
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volunteer
So what would the Y value be?
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student
0
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volunteer
Yeah
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volunteer
Um, OK. So basically, the first point would be 00. OK.
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volunteer
Yeah, and then
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volunteer
if we have one, what would 5 be?
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student
We live to get um
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student
we to get um one positive one from.
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volunteer
Um,
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volunteer
oh, where did I get it from?
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student
Yeah
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volunteer
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 c...
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student
Oh, OK, OK.
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volunteer
Yeah.
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volunteer
So
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volunteer
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.
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student
OK
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volunteer
So, um, if we had
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volunteer
if the X value is 1, then what do you think the Y value would be?
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student
Uh, negative 1.
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volunteer
Yeah, so then we would have one common negative one. So then that would be over here.
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volunteer
OK. Um, OK, now let's do
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volunteer
2
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volunteer
Um
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volunteer
so if we add 2, then what would the XB?
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