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Alright, the most generic
version of a quadratic

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function definition is on
your paper, but it's some

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number AX squared plus
some number BX plus some

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constant C. So, that's just
generic, you guys. A, B,

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and C are numbers
essentially. That's just a

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very generic version of any
original quadratic we could

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look at. In generic terms,

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what would the rate of
change function be?

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[AX plus B]

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Just AX plus B? Sabrina?

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2AX plus B?

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2AX plus B?

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Go ahead and look back at
the ones that we already

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talked about. So far I've
heard AX plus B, I've heard

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2AX plus B. People
can either confirm

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or deny one of those,

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or propose something
totally different.

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[I think the second
one's right]

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Casey wants to jump on
Sabrina's bandwagon?

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Who says I'm with Gromick,
it's AX plus B? He's got

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his supporters. Who says
I'm with Sabrina. It's 2AX

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plus B. Who says I just
don't know yet. Oh wait,

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Gromick, what did
you just do?

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[I think it's 2
times AX plus B.]

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Gromick just left his own
bandwagon. I'm worried for

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your supporters, Gromick.
Gromick just left his own

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bandwagon. The Gromick
supporters, now what? You

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wanna hold strong, or do
you want to follow your

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fearless leader? Gromick,
how come you changed your

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mind? How come your
changed your mind?

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[Because I'm the
last one to get A,]

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[you have to times it by
a 2 to get it squared.]

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[So, that's why
I changed my mind.]

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Ryan?

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[Mmm hmm]

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Mmm hmm, for now?

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[Well, doesn't like A
represent a number]

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Mmm hmm

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[So, I think the
answer's right]

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That's actually a
really good point.

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A does represent a
number, so how about this.

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What is the A value
of this quadratic?

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[1]

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Careful

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[Negative 1]

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Negative 1. You can draw
it in if you want to.

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Negative 1 is the A value.
Here was the rate of

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change. Is it simply
the original AX plus B,

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or is it twice the
A value X plus B?

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[twice]

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Twice. What's the A value
here? It's not written.

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[1]

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AX plus B, or 2AX plus B?

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[2]

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2, good. Here's the scoop.
The rate of change for

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these quadratics, you've
seen enough, that they end

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up being linear. But you
can actually come up with

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the rate of change equation
without drawing the step

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functions, without even
graphing them at all. You

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can go straight from the
original quadratic to it's

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rate of change function
using the pattern

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that you guys just noticed.