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There actually is a spot on
your worksheet to write

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down the left side equation.
Yesterday, I even busted

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out a ruler and drew in
the left-hand version of that

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rate of change graph. Then
we actually calculated, not

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calculated, I'm sorry.
We actually found and

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discussed the
equation for that line.

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Did anybody write it down? Do you remember it?

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[Y equals negative 2X]

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[Plus 7]

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Plus what?

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[5]

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5. All we did was figure out
change in Y, change in X.

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That made our rate of
change. Then we needed

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our initial value which was
at 5. Then we did the same

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thing for the right-hand
version of this. So, right-

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hand...and, whoops, bad
timing. Something like that.

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We calculated, or found,
discussed, whatever the

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equation for that one
as well. What was...?

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[Y equals negative
2X plus 7]

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Negative 2X plus

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[7]

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7. Like I said, there's
an actual spot on your

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worksheet, you may go
ahead and put those in.

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Last, but certainly not
least, we talked about the

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accurate one. You guys
guessed where you thought

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it would be, and then I went
ahead and took my slider

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and zipped it down to
the smallest step that this

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program lets me do.

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[There's a little lag there]

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What's that Ryan? Oh,
why it didn't want to graph?

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Hang on

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[What about
those little...like...]

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Little steps? Yeah, those
are baby steps at, you can't

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see it, 0.2. Those are baby
steps at 0.2, but it allows us

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to see what that line is
approaching at least if we

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could go even smaller baby
steps, and we wrote that

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equation as well,
which was Y equals...

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[Negative 2]

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Negative 2X plus 6. So
that's the one that we want

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to end up talking about because, again, it's the

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most accurate. The other
two are based off of step

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size 1, so you're assuming
a lot, because you're

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holding stuff constant for a
whole unit when we know

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there's a whole bunch of
values in between there,

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that we've ignored
essentially. So, this is the

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one that we want to end up
talking about. Where we left

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off yesterday was making
this connection- the original

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quadratic that this was
based off of is the Y equals

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negative X squared plus 6X
minus 4. And the accurate

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rate of change equation
that came out of it

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was negative 2X plus 6.