Answer
$f(x)=-x^2(x+3)(x-2)$
Work Step by Step
Step 1. Based on the given graph, we can identify the real zeros as $x=-3$ (multiplicity 1), $x=0$ (multiplicity 2), and $x=2$ (multiplicity 1).
Step 2. We can write a general form of the polynomial as $f(x)=a(x+3)(x^2)(x-2)$ where $a$ is unknown.
Step 3. Use the given point $(-2,16)$ on the curve, we have $f(-2)=a(-2+3)(-2)^2(-2-2)=16$, thus $a=-1$
Step 4. Thus the function is $f(x)=-x^2(x+3)(x-2)$
