Datasets:
NationalTutoringObservatory
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MathEd-PII

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volunteer
I'm reading...
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volunteer
C is correct.
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student
oh nooo
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student
okay thank you
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student
is it because the data points
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student
have the biggest gap
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student
from the mean
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volunteer
Yes. For (C), the data points are the furthest away from the mean. The "spread" is the greatest.
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student
Okay I understand
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student
thank you
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student
that will be all
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student
have a good day :D
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volunteer
You as well.
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volunteer
Hi!
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student
hi
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volunteer
one second
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volunteer
Hey, can you hear me?
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student
yea
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volunteer
OK. Um, OK, so.
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volunteer
first we need to understand the shape of the graph. So the graph is a para uh parabola, right? And the negative sign is just showing that this graph is opening.
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volunteer
downward
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volunteer
upside down you
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volunteer
The coefficient to makes it narrower and steeper, right? So this is just gonna be the original function. We're trying to make it into this Y equals function right here. So now we know that the graph needs to open downward, and the two makes it more steep. The vertex is still going to be at 00. So what we're gonna do is...
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volunteer
equ ation we have 2 x^2, um, can you go ahead and plug in 0 and tell me what you get.
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volunteer
for the X value.
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volunteer
So if we were to replace the X with 0.
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student
I
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student
I
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student
I
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student
Um, I'm sorry. I'm kinda confused.
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volunteer
That's OK
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student
OK
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student
OK.
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volunteer
Um, I'm just gonna go ahead and walk you through it, OK? So,
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volunteer
if we have Y equals -2 x^2. Basically we're just plugging in a point to check, oh, if I put in this point, what would I get for the Y value, right? So if I were to do -2
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volunteer
and then I replaced the X with a 0, and I put a square. What is 02? So 0 times 0.
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student
Uh, 0, right?
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volunteer
Yeah, exactly. So it'd just be Y equals 2 times 0, and anything times 0 is just gonna be
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volunteer
0, right?
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student
Yeah
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volunteer
OK, so this is just gonna be 0. So basically what we're saying is when we plug in 0, which is our X, our result is also going to be 0.
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volunteer
Do you understand how I got this coordinate point?
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student
Yeah
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volunteer
OK, perfect. So now what we're gonna do is on the real graph, we're going to go and put the point at 00.
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student
Mhm.
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volunteer
OK
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volunteer
And the next thing that we're gonna do is we're gonna plug in another point. So let's do, let's plug in one.
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volunteer
OK? So if we were to do Y equals -2.
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volunteer
x 1
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volunteer
2. What is 1 times 1 or 1 squared.
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student
Uh, one
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volunteer
Exactly, so it's just gonna be one. So then what's 2 times just one.
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student
Um
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student
that'd be -2, right?
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volunteer
Yeah, it would be negative too. Perfect. So, now we know that when we plug in one, what would our Y coordinate be?
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volunteer
Here's a hint, you just said it.
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student
2
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volunteer
Mhm, yeah. So now we know another point, right? 1 and -2.
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volunteer
So now we're gonna do another
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volunteer
um Basically what we're doing is
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volunteer
we can see that the graph up here is, it looks very similar to just Y equals 2 x 2, and we can see the same points, we can see one.
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volunteer
and one is matched up because right here at this point right here, that's 11. This point right here is
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volunteer
2.4. And if we already see a pattern here with one
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volunteer
2.
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volunteer
We can also just see that since it's gonna be the same, a parabola is always gonna be like even, right? It's always or not even, it's always gonna like be symmetric.
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volunteer
So if there's a point here, we need to make it even so on this side of the graph right here, where could I put a point that would match up with this one.
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student
Uh, -1, 2, right?
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volunteer
Mhm. Perfect. Yeah. So that's right. And then
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volunteer
it looks like they want us to, so it says move the red points.
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volunteer
to moving the red points changes the vertical stretch or compression, moving the blue point shifts the function left, right, up or down. So it's, so do you see how like when we have a normal function, we would usually have something like, or not a normal function, but if we're moving left or right, we would usually hav...
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student
Mhm.
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volunteer
Yeah, we would have something like that, right? And this function, we don't have that, so we're not moving left or right. And we also don't have like a plus or minus value at the end.
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volunteer
So
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volunteer
basically, all you're really doing is you're just changing the slope to be negative 2.
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student
OK
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volunteer
So, let's plug in another point. Over here they're doing 2 and 4. Let's just go ahead and do 2, OK? So if we were to plug into
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volunteer
so if we were to do Y equals -2.
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volunteer
times 22. What is 22 or 2 times 2?
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student
04
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volunteer
Mhm, 4, so then we would have Y equals -2 x 4. What's 2 times 4?
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student
Uh, -8, right?
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volunteer
Mhm, yeah, you're right. So it'd be -8. So now when we plug in, what's our output?
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student
Um, it would be.
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volunteer
Remember you just said it
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student
-8, right?
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volunteer
Mhm, yeah, exact
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student
OK.
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volunteer
So it'd be 28, and we could put that as a point on the graph, and where would like the matching point before it?
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student
Uh, 8 or 28.
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volunteer
Mhm. Perfect. So just be right here. And then we could just go ahead and now we can form our parabola and just draw it out. So honestly, all we really did is we plugged in different points.
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volunteer
and we got this. You can plug in any numbers. So we just did 0
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volunteer
1 and 2, but you can do anything. You can do like
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volunteer
preferably you want to plug in like something on the X axis, right? You want to do like -10
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volunteer
all the way up until 10, like any value here. You don't want to do like 32.
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volunteer
You want to do something here and then hopefully it'll match up.
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volunteer
on the graph
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student
All right
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volunteer
Yeah, so let me know if you have any other questions or anything else that I can help you with.
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student
Um
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student
yeah, no, I think I get it now. Thank you.
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