Answer
Refer to the graph below.
Work Step by Step
The $x$-intercepts of the function's graph can be found by equating each factor to zero then solving each equation to obtain:
\begin{align*}
(x+2)^2&=0 &\text{or}& &(x-3)^2=0\\
x+2&=\pm\sqrt0 &\text{or}& &x-3=\pm\sqrt0\\
x+2&=0 &\text{or}& &x-3=0\\
x&=-2 \text{ (multiplicity 2)} &\text{or}& &x=3 \text{ (multiplicity 2)}\\
\end{align*}
Thus, the $x$-intercepts are $-2 \text{ and } 3$.
The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$:
\begin{align*}
P(0)&=\frac{1}{12}(0+2)^2(0-3)^2\\
&=\frac{1}{12}(4)(9)\\
&=\frac{36}{12}\\
&=3
\end{align*}
Thus, the $y$-intercept is $3$.
Create a table of values to obtain the one below.
Then, plot each ordered pair and connect the points using a smooth curve.
Refer to the graph above.
