Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Cumulative Review Exercises - Page 880: 22

Answer

The graph is shown below:
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Work Step by Step

We have to plot the graph of the function $ f\left( x \right)={{\left( x+2 \right)}^{2}}-4$; put y in place of $ f\left( x \right)$ and evaluate the value of the y variable for each value of the x variable or the value of the x variable for each value of the y variable: And to find the value of the y-intercept, substitute $ x=0$ as given below: $\begin{align} & y={{\left( x+2 \right)}^{2}}-4 \\ & ={{\left( 0+2 \right)}^{2}}-4 \\ & =4-4 \\ & =0 \end{align}$ To find the value of the x-intercept, substitute $ y=0$ as given below: $\begin{align} & 0={{\left( x+2 \right)}^{2}}-4 \\ & 0+4={{\left( x+2 \right)}^{2}}-4+4 \\ & {{\left( x+2 \right)}^{2}}=4 \\ & \left( x+2 \right)=\sqrt{4} \\ & x+2=\pm 2 \\ & x=\pm 2-2 \\ & x=0,-4 \end{align}$ To find the value of the y-intercept, substitute $ x=-2$ as given below: $\begin{align} & y={{\left( -2+2 \right)}^{2}}-4 \\ & ={{0}^{2}}-4 \\ & =0-4 \\ & =-4 \end{align}$ Plot the intercepts $\left( 0,0 \right),\left( -4,0 \right)\text{, and }\left( -2,-4 \right)$ and join them with a free hand in order to get the graph of equation $ y={{\left( x+2 \right)}^{2}}-4$:
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