College Algebra, Chapter 2, 2.2, Section 2.2, Problem 22

Make a table of values and sketch the graph of the equation $y = 9 - x^2$. Find the $x$ and $y$ intercepts.

$ \begin{array}{|c|c|}
\hline\\
\text{Let } x & y = 9 - x^2 \\
\hline\\
-3 & 0 \\
\hline\\
-2 & 5 \\
\hline\\
-1 & 8 \\
\hline\\
1 & 8 \\
\hline\\
2 & 5 \\
\hline\\
3 & 0\\
\hline
\end{array} $

To solve for $x$ intercept, we set $y = 0$


$
\begin{equation}
\begin{aligned}

0 =& 9 - x^2
\\
\\
x^2 =& 9
\\
\\
x =& \pm \sqrt{9} = \pm 3

\end{aligned}
\end{equation}
$


Thus, the $x$ intercept is at $(-3,0)$ and $(3, 0)$


$
\begin{equation}
\begin{aligned}

y =& 9 - 0^2
\\
\\
y =& 9

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0, 9)$