options: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
problem_activity: Problem 1
Below is the parent function of a quadratic function:
[IMG]
Given the equation in vertex form and the corresponding graph, identify the transformations to each function.
| **           Equation          ** |                             **           Graph          **                              | **           Transformation(s)          ** |
|-----------------------------------|-----------------------------------------------------------------------------------------|--------------------------------------------|
|       $${g(x)=(x+1)^2+3}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1b.png |                                            |
|       $${r(x)=-2(x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1c.png |                                            |
|        $${t(x)=(2x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1d.png |                                            |
Problem 2
A quadratic equation is
decreasing over the interval
$${-\infty < x < 3}$$
increasing over the interval
$${3 < x < \infty}$$
and has a rate of change of zero at
$${x=3}$$
.
Describe how each of the three graphs below fit this description.
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2a.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2b.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2c.png |
|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|


correct_option_index: 2