Chapter 1.6, Problem 21E

Solution

To sketch the graph of $f$ , $g$ and $h$ by hand. Support the answer with a grapher.

Given:

  $\begin{array}{l}f\left(x\right)={\left(x+2\right)}^2\\ g\left(x\right)=3x^2-2\\ h\left(x\right)=-2{\left(x-3\right)}^2\end{array}$

Calculation:

  $f\left(x\right)={\left(x+2\right)}^2$

Let $f\left(x\right)=y$. Make table of values as follows:

  

  $g\left(x\right)=3x^2-2$

Let $g\left(x\right)=y$. Make table of values as follows:

  

  $h\left(x\right)=-2{\left(x-3\right)}^2$

Let $h\left(x\right)=y$. Make table of values as follows:

  

Graph:

  

Verify the graphs using a grapher:

  

Hence, verified.