Find the $x$-intercept(s) and the $y$-intercept(s) of the graph of $y=x^{2}-4$.

Solution  To find the $x$-intercept(s), we let $y=0$ and solve the equation $$\begin{array}{rl@{{16pt}}l} x^{2}-4=0 & & \\[3pt] ( x+2) ( x-2) =0 & & {\color{#0066A7}{\hbox{Factor.}}} \\[3pt] x=-2{\rm \quad or \quad } x=2 & & {\color{#0066A7}{\hbox{Set each factor equal to 0 and solve.}}} \end{array}$$

The equation has two solutions, $-2$ and $2$. The $x$-intercepts are $-2$ and $2$.

To find the $y$-intercept(s), we let $x=0$ in the equation. $$y=0^{2}-4=-4$$

The $y$-intercept is $-4$.