Answer
The graph is shown below:
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$:
