Answer
Refer tot he 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&=0 &\text{or}& &(x+1)^2=0& &\text{or}& &2x-3=0\\
x&=-2 &\text{or}& &x+1=\pm\sqrt0& &\text{or}& &2x=3\\
x&=-2 &\text{or}& &x+1=0& &\text{or}& &x=\frac{3}{2}\\
x&=-2 &\text{or}& &x=-1 \text{ (multiplicity 2) }& &\text{or}& &x=\frac{3}{2}\\
\end{align*}
Thus, the x-intercepts are $0, -1, \text{ and } \frac{3}{2}$.
The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$:
\begin{align*}
P(0)&=(0+2)(0+1)^2(2\cdot0-3)\\
&=2(1^2)(-3)\\
&=-6(1)\\
&=-6
\end{align*}
Thus, the $y$-intercept is $-6$.
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.
