Answer
$f(x)=-2 (x+4)(x+1)(x-2)$
Work Step by Step
Let us consider that $a$ is a zero of a function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$.
Therefore, we can write the equation of the function as:
$f(x)=k (x+4)(x+1)(x-2).(1)$
Since, $(0,16)$ lies on the graph, so we have:
$k(4)(1)(-2) =16\\ -8k = 36 \\k=-2$
Thus, equation (1) becomes:
$f(x)=-2 (x+4)(x+1)(x-2)$
