Chapter 1.2, Problem 24AYU

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 24AYU

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

Explanation of Solution

Given:

The equation $y=-x^2+1$

Calculation:

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

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

$1=x^2$

$\pm 1=x$

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

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

$y=1$

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