Answer
The graph is shown below
Work Step by Step
The graph of $y={{x}^{2}}-9$ consists of points $\left( x,y \right)$.
To graph the equation $y={{x}^{2}}-9$, plot some points $\left( x,\,y \right)$ and join them. To find some points $\left( x,\,y \right)$, choose random $x$ values, and find the corresponding $y$ values by using the equation $y={{x}^{2}}-9$.
If $x=0$, then $y={{\left( 0 \right)}^{2}}-9=-9$. Therefore, the point $\left( 0,-9 \right)$ is on the graph.
If $x=1$, then $y={{\left( 1 \right)}^{2}}-9=-8$. Therefore, the point $\left( 1,-8 \right)$ is on the graph.
If $x=-1$, then $y={{\left( -1 \right)}^{2}}-9=-8$. Therefore, the point $\left( -1,-8 \right)$ is on the graph.
If $x=-3$, then $y={{\left( -3 \right)}^{2}}-9=0$. Therefore, the point $\left( -3,0 \right)$ is on the graph.
If $x=-5$, then $y={{\left( -5 \right)}^{2}}-9=16$. Therefore, the point $\left( -5,16 \right)$ is on the graph.
If $x=5$, then $y={{\left( 5 \right)}^{2}}-9=16$. Therefore, the point $\left( 5,16 \right)$ is on the graph.
Draw the graph by plotting these points and connecting them.
The graph of the equation $y={{x}^{2}}-9$ represents the equation of a parabola.
