Finding the Intercepts of a Graph

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 \(-4\).