Chapter 1.2, Problem 21AYU

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

$y=x^2-1$

To determine

To find: The intercepts and graph of the equation $y=x^2-1$.

Answer to Problem 21AYU

$x\text{-intercept }=\mathrm{ \pm 1}, y\text{-intercept }=-1$

Explanation of Solution

Given:

The equation $y=x^2-1$

Calculation:

To find the $x\text{-}\mathrm{intercept}$, let $y=0$ implies $x^2-1=0$

$x^2-1+1=0+1$Add 1 to both sides

$x^2=1$

$x=\pm 1$

$x\text{-}\mathrm{intercept}$ are $\pm 1$

To find the $y\text{-}\mathrm{intercept}$, let $x=0$ implies $y={(0)}^2-1$

$y=-1$

$y\text{-}\mathrm{intercept}$ is$-1$