Chapter 1.1, Problem 12E

To determine

To graph: The given function and its parent function and then to describe the transformation.

Answer to Problem 12E

The graph of $h(x)={(x+4)}^2$ is a horizontal translation $4$ units left the graph of the parent quadratic function.

Explanation of Solution

Given information: Given function is $h(x)={(x+4)}^2$ .

Graph:

The function $h$ is a quadratic function. Using a table of values to graph the given function and the parent function $g(x)=x^2$ ,

  $\begin{array}{lll}x\hfill & y=x^2\hfill & y={(x+4)}^2\hfill \\ -2\hfill & 4\hfill & 4\hfill \\ -1\hfill & 1\hfill & 9\hfill \\ 0\hfill & 0\hfill & 16\hfill \\ 1\hfill & 1\hfill & 25\hfill \\ 2\hfill & 4\hfill & 36\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $h$ (shown by blue colored line) is a horizontal translation $4$ units left the graph of the parent quadratic function $g(x)=x^2$ (shown by green colored line).

So, the graph of $h(x)={(x+4)}^2$ is a horizontal translation $4$ units left the graph of the parent quadratic function.