Chapter 1.1, Problem 32E

To determine

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

Answer to Problem 32E

The graph of $f(x)=4x^2-3$ is vertical stretch by a factor of $4$ and a vertical translation of $3units$ down with respect to the graph of the parent quadratic function.

Explanation of Solution

Given information: Given function is $f(x)=4x^2-3$ .

Graph:

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

  $\begin{array}{lll}x\hfill & g(x)=x^2\hfill & f(x)=4x^2-3\hfill \\ -2\hfill & 4\hfill & 13\hfill \\ -1\hfill & 1\hfill & 1\hfill \\ 0\hfill & 0\hfill & -3\hfill \\ 1\hfill & 1\hfill & 1\hfill \\ 2\hfill & 4\hfill & 13\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $f$ (shown by blue colored line) is a vertical stretch by a factor of $4$ and a vertical translation of $3units$ down w.r.t. the graph of the parent quadratic function $g(x)=x^2$ (shown by green colored line).

So, the graph of $f(x)=4x^2-3$ is a vertical stretch by a factor of $4$ and a vertical translation of $3units$ down with respect to the graph of the parent quadratic function.