## Precalculus (6th Edition) Blitzer

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 $y={{\left( x+2 \right)}^{2}}-4$: