There are two $x$-intercepts: $-3$ and $3$. The y-intercept is $-9$. See the graph below.
Work Step by Step
In order to find the $x$-intercept, we have to plug $y=0$ into the equation, and the $x$-coordinate will give us the intercept itself. $y=x^2-9$ $0=x^2-9$ $x^2=9$ $x=\pm3$ The same thing should be done for the $y$-intercept, however, here $x=0$ should be plugged into the equation. $y=x^2-9$ $y=0^2-9$ $y=-9$ There are two x-intercepts: $-3$ and $3$ The y-intercept is $-9$ Few other points that will help us plot the graph: If $x=1$ $y=1^2-9=-8$ The point $(1,-8)$ is on the graph. If $x=-1$ $y=(-1)^2-9=-8$ The point $(-1,-8)$ is on the graph. If $x=4$ $y=4^2-9=7$ The point $(4,7)$ is on the graph.