Precalculus, Chapter 1, 1.2, Section 1.2, Problem 24

Determine the intercepts and graph equation $y = -x^2 + 1$ by plotting points. Be sure to label the intercepts.

$x$-intercept:


$
\begin{equation}
\begin{aligned}

y =& -x^2 + 1
&& \text{Given equation}
\\
0 =& -x^2 + 1
&& \text{To find the $x$-intercept, we let } y = 0
\\
x^2 =& 1
&&
\\
x =& \pm 1
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(1,0)$ and $(-1,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,1)$