Find the $x$-Intercepts

The $x$-intercepts of the graph of an equation occur when $y=0$.

Example 1

For the equation $y=(x-9)(x+2)$, look at the factors $(x-9)$ and $(x+2)$.

Notice in the first factor, $(x-9)$, $x=9$ makes the factor equal to 0.

Substitute 9 for $x$ in the equation.

$y=(9-9)(9+2)$

$y=(0)(11)$

$y=0$

Notice in the second factor, $(x+2)$, $x=-2$ makes the factor equal to 0.

Substitute -2 for $x$ in the equation.

$y=(-2-9)(-2+2)$

$y=(-11)(0)$

$y=0$

In the equation $y=(x-9)(x+2)$, $y=0$ when $x=9$ and $x=-2$.

The $x$-intercepts occur when $x=9$ and $x=-2$.

To find the $x$-intercepts of a quadratic equation in factored form, set each factor equal to zero and solve for $x$.

Example 2

Find the $x$-intercepts for $y=(2x+7)(x-4)$.

The $x$-intercepts occur when $y=0$.

Set each factor to 0 and solve.

$\begin{array}{ccccc}\hfill 2x+7& \hfill =\hfill & 0x-4\hfill & \hfill =& \hfill 0\hfill \\ \hfill x& \hfill =\hfill & -3.5x\hfill & \hfill =& \hfill 4\hfill \end{array}$