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 $(0,1)$