Answer
$f(x)=x^4 - 4 x^3 + 5 x^2 - 2 x$
Work Step by Step
If $c$ is a zero of a function with multiplicity $b$ then $(x-c)^b$ is a “factor” of the function.
We can see that $0$, $1$ and $2$ are zeros and that the graph remains negative at both sides of $2$ (it touches and doesn't cross the x-axis, hence its multiplicity is even, e.g. $2$), hence $f(x)=ax(x−1)^{2}(x−2)=a(x^4 - 4 x^3 + 5 x^2 - 2 x).$
If $a=1$, $f(x)=x^4 - 4 x^3 + 5 x^2 - 2 x$ can be a possible function.
