Answer
$f(x)=-x(x+3)^2(x-3)^2$
Work Step by Step
Step 1. Based on the given graph, we can identify the real zeros as $x=-3$ (multiplicity 2), $x=0$ (multiplicity 1), and $x=3$ (multiplicity 2).
Step 2. We can write a general form of the polynomial as $f(x)=a(x+3)^2(x)(x-3)^2$ where $a$ is unknown.
Step 3. Use the given point $(2,-50)$ on the curve, we have $f(2)=a(2+3)^2(2)(2-3)^2=-50$, thus $a=-1$
Step 4. Thus the function is $f(x)=-x(x+3)^2(x-3)^2$
