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Get me started. Here I
am, I have a quadratic.

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I wanna find it's vertex,

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I don't know what to
do, somebody help me.

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Gregory?

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[The rate of
change function]

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OK, why, Gregory, would
I want the rate of change

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function to help
me find a vertex?

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[So you can get the X]

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OK, how about this. I'll
make one up really quick.

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Let's do that instead.
Sure, I made that up. Greg

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says I need the rate of
change equation, so what's

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the rate of change
equation for this?

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[2X minus 10]

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Alright, I found the
rate of change equation,

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who cares? Somebody
other than Greg?

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Somebody other than
Gromick too. Sabrina.

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[That's how you
get the zero]

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Why in the world
would I do that?

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I mean it's all fine
and dandy, but why?

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[You're trying to find
the Y value at zero.]

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OK, so, why is it, and
I'm actually going to let

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Sabrina back off the hook
because she got me this

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far. Why is it that my
vertex is going to happen

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when rate of change equals
zero? What's going on with

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Y values being zero on the
rate of change graph to

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where that's going to
lead me to vertex?

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Again, I can do
it, but why? Ryan?

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[It's where it crosses
the X-axis.]

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That's where it crosses the
X-axis, hence the Y-value

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being zero, but why is that

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the location of
vertex? Marissa?

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[It's the transite to make
the positive or negative,]

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[or increase or decrease.]

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Tell me more about it
being the turning point to

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positives or negatives,
just elaborate

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[Once it hits the
X-axis, it can either]

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Are you picturing
a line in your head?

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[Yeah. And on the X-axis, like right where it hits]

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[the X-axis, it was a
negative increase, then it]

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[has a positive increase
after it hits the X-axis]

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OK, what does that mean for
the curve? The fact that

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prior to this X-intercept
it's negative,

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and after that X-intercept
it's positive?

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[That's where the curve's
turning point is gonna be.]

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And in this case, what
is it turning from,

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from what to a what?

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[It's...it looks like a
U. Increase and then.]

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[It's a negative increase]

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[and it goes from a
positive increase.]

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OK, so draw a U.
So, tell me again,

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[It goes from a positive]

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So you read a graph
like a book.

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It changes from
what to what?

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[Negative to positive.]

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The rate of change changes
from a negative to a

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positive. What's the curve
gonna do? Change from?

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[Negative to positive?]

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What does negative mean on
the curve? Negative rate of

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change, decrease, good.
Very good. Alright, Marissa

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brought it home. Ladies and
gents, setting it equal to

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zero, this whole idea of X-
intercept, yes. But that is

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when your rate of change
changes. In this case,

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Marissa said that it's a
negative rate of change

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prior to that spot, and
then it's a positive rate

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of change after that spot.
That's when your curve

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turns. In this case from
decrease to increase. Very

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good. Setting it equal to
zero, that's your rate of

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change being zero turning
point, exactly. I can solve

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this in my head, I get X
equals 5. Sweet. Is that my

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vertex? I got X equals 5.
Done! Why not, Amy Lynn?

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[Because you're not.]

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[Just because you're not.]

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[Just because you're not?]

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Just because. Well, if I'm
just not done, there's got

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to be a reason why
I'm not done

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[Plug it in]

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Why would I plug it in?
That's just more work.

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Why would I go there?

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I might even need a
calculator for that.

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[You have to]

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Why?

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[To get the other point]

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To get what other point?

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[The Y-value]

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Why do I want the Y-value?

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[It gets the vertex]

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Ladies and gents,
your vertex is a what?

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[A point]

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It's a point. It's an
ordered pair, yes. I might

90
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know that it happens at 5
now. But 5 comma what? Is

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my vertex at 5 comma a
hundred? Is it at 5 comma

92
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negative 10? I don't know. I know it's a 5. But that's

93
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not your vertex. That's
the start of your vertex

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perhaps. So, you plug it back in. X squared minus

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10X plus 5. 25 minus 50
plus 5. So, negative 25

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plus 5, negative 20. OK,
I got a vertex. Cool.

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Is it a max or a min?