Chapter 1.2, Problem 22AYU

In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.

$y=x^2-9$

To determine

To find: The intercepts and graph of the equation $y=x^2-9$.

Answer to Problem 22AYU

$x\text{-intercept }=\mathrm{ \pm 3}, y\text{-intercept }=-9$

Explanation of Solution

Given:

The equation $y=x^2-9$

Calculation:

To find the $x\text{-}\mathrm{intercept}$, let $y=0$ implies $x^2-9=0$

$x^2-9+9=0+9$Add 9 to both sides

$x^2=9$

$x=\pm 3$

$x\text{-intercept}$ are $\pm 3$

To find the $y\text{-intercept}$, let $x=0$ implies $y={(0)}^2-9$

$y=-9$

$y\text{-intercept}$ is$-9$