Answer
$f(x)=x^3−3x^2+2x$
Work Step by Step
If $c$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “factor” of the function.
We can see from the graph that $0$, $1$ and $2$ are zeros of the function.
Hence,
$f(x)=a(x-0)(x−1)(x−2)\\
f(x)=a(x^3−3x^2+2x)$
When $a=1$, the function becomes
$f(x)=x^3−3x^2+2x$
Thus, one possible polynomial function that might have the given graph is
$f(x)=x^3−3x^2+2x$
