# X-intercepts Y-intercepts

$x$-intercepts when $y=0$
$y$-intercepts when $x=0$

### Example 1

Sketch the graphs of $y=x^2+x-2$ by stating $x$- and $y$-intercepts.

$x$-intercepts when $y=0$
\begin{align} \displaystyle x^2+x-2 &= 0 \\ (x+2)(x-1) &= 0 \\ x &= -2, 1 \\ \end{align}
$y$-intercepts when $x=0$
\begin{align} \displaystyle y &= 0^2+0-2 \\ &= -2 \\ \end{align}

### Example 2

Sketch the graphs of $y=-x^2+3$ by stating $x$- and $y$-intercepts.

$x$-intercepts when $y=0$
\begin{align} \displaystyle -x^2+3 &= 0 \\ x^2 &= 3 \\ x &= -\sqrt{3}, \ \sqrt{3} \\ \end{align}
$y$-intercepts when $x=0$
\begin{align} \displaystyle y &= -0^2+3 \\ &= 3 \\ \end{align}