Chapter 9.2, Problem 2BGP

To determine

To graph and describe translation of the function in relation to the graph of $f(x)=x^2$ .

Explanation of Solution

Given information :

The function that is provided: $g(x)={(x+2)}^2$ .

Graph :

Interpretation :

The graph represented by $g(x)={(x-h)}^2$ is equivalent to the graph of $f(x)=x^2$ that has been translated horizontally. The direction of translation or movement of the graph is dependent on the value of $h$ .

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

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

In the function $g(x)={(x+2)}^2$ , the value of $h<0$ at $h=-2$ . Therefore, the translation of the function with respect to the graph of $f(x)=x^2$ , as seen in the graph shown above, is 2 units to the left.