Chapter 9.2, Problem 32PPS

To determine

To select function corresponding to the graph shown.

Answer to Problem 32PPS

Graph 1 corresponds to − $y=x^2-4$

Graph 2 corresponds to − $y=x^2+2$

Explanation of Solution

Given information :

The functions that is are provided: $y=x^2-4$ and $y=x^2+2$

The graph represented by $g(x)=x^2+k$ is equivalent to the graph of $f(x)=x^2$ that has been translated vertically. The direction of translation or movement of the graph is dependent on the value of k .

If $k>0$ , the graph of $f(x)=x^2$ is translated $\left|k\right|$ units upwards.

If $k<0$ , the graph of $f(x)=x^2$ is translated $\left|k\right|$ units downwards.

Hence, Graph 1 has a vertex below the origin and therefore corresponds to $y=x^2-4$ where $k<0$ at $k=-4$ while Graph 2 corresponds to $y=x^2+2$ where $k>0$ at $k=2$ .