Chapter 9.2, Problem 33PPS

To determine

To select function corresponding to the graph shown.

Answer to Problem 33PPS

Graph 1 corresponds to − $y=-\frac{1}{3}{x}^2$

Graph 2 corresponds to − $y=-2x^2$

Explanation of Solution

Given information :

The functions that is are provided: $y=-\frac{1}{3}{x}^2$ and $y=-2x^2$

The graph of quadratic function $f(x)$ when multiplied by a positive constant a , the resulting graph $af(x)$ is a vertical dilation of $f(x)$ . The function is stretched or compressed vertically by a factor of $\left|a\right|$ .

If $\left|a\right|$ $>1$ , the graph of $f(x)$ is stretched vertically, that is, all points on the graph $f(x)$ move farther away from the x -axis.

If $\left|a\right|<1$ , the graph of $f(x)$ is compressed vertically, that is, all points on the graph $f(x)$ move closer to the x -axis.

Hence, Graph 1 is vertically compressed and therefore corresponds to $y=-\frac{1}{3}{x}^2$ where $\left|a\right|<1$ at $a=-\frac{1}{3}$ while Graph 2 is vertically stretched and corresponds to $y=-2x^2$ where $a=-\frac{1}{3}$ at $a=-2$ .