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-3)^2&=0 &\text{or}& &(x+1)^2=0\\
x-3&=\pm\sqrt0 &\text{or}& &x+1=\pm\sqrt0\\
x-3&=0 &\text{or}& &x+1=0\\
x&=3 &\text{or}& &x=-1 \text{ (multiplicity 2)}\\
\end{align*}
Thus, the $x$-intercepts are $-1 \text{ and } 3$.
The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$:
\begin{align*}
P(0)&=(0-3)^2(0+1)^2\\
&=(-3)^2(1^2)\\
&=9(1)\\
&=9\end{align*}
Thus, the $y$-intercept is $9$.
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.
