PR1 addition

[AbbyANoble]

Connect Definition 4.1.9 and Observation 4.1.10
by completing the square on the standard form to see the vertex form pop out. Maybe here or maybe as an aside to an appendix?

[tdegeorge]

Submitted a pull request (Fixed PR1 Issues #382) - didn't want to start another branch and did it at the same time.

I added an activity to have students convert from standard to vertex. Does that work?

[AbbyANoble]

I added an activity to have students convert from standard to vertex. Does that work?

I mentioned this mostly to build the idea in general. To develop the fact that the x value of the vertex is -b/2a by completing the square on y=ax^2+bx+c, not a specific quadratic. Currently, the text just says x=-b/2a without any reasoning behind it, so I thought completing the square to get to vertex form would show that -b/2a pop up where we expect the h in vertex form.

As is, it seems like this activity is encouraging students that the way to find the vertex and aos of a standard form quadratic is by completing the square, which is not we'd actually want students to do.

I mentioned this could be in an appendix because maybe it's too in the weeds for a lot of people since there is a lot of algebraic manipulation of the a, b, and c. Or if it's in the text, maybe show the whole thing, and then ask what the x-value of the vertex is?