College Algebra, Chapter 2, 2.3, Section 2.3, Problem 18

Determine an appropriate viewing rectangle for the equation $y = x(x+6)(x-9)$ and use it to draw the graph.

We can determine the appropriate viewing rectangle easier by getting the $x$ and $y$-intercept at the equation. So, if we set $y=0$

$
\begin{equation}
\begin{aligned}
0 &= x(x+6)(x-9) && \text{Solve for } x\\
\\
x &= 0 , x = -6 \text{ and} x =9
\end{aligned}
\end{equation}
$

Thus, the $x$-intercept are at $(0,0), (-6,0)$ and $(9,0)$

Next, solving for $y$-intercept, where $x = 0$

$
\begin{equation}
\begin{aligned}
y &= 0(0+6)(0-9)\\
\\
y &= 0
\end{aligned}
\end{equation}
$


The $y$-intercept is at $(0,0)$
Hence, we assume that the appropriate viewing rectangle is $[-10,10]$ by $[-300,300]$