Chapter 9.2, Problem 48PFA

To determine

To find the equation of the second graph based on the parent graph.

Answer to Problem 48PFA

C. $f\left(x\right)=-\frac{1}{3}{x}^2$ and D. $f\left(x\right)=-\frac{2}{3}{x}^2$ .

Explanation of Solution

Given information :

The parent graph is given by the function $f\left(x\right)=x^2$ .

To reflect the graph over x-axis, change the existing sign of the function. That is, $-f\left(x\right)$ . This will give the make the equation of the reflected graph as $-f\left(x\right)=-x^2$ .

Next, to compress the parabola vertically, the coefficient of $x^2$ must be less than the present coefficient. In this case, it needs to be less than 1. Since 1 is the coefficient of $x^2$ .

Thus, there are two option which math these two criteria. Options C and D.