Answer
$5 x^4 - 10 x^2 + 5
$
Work Step by Step
If $a$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “multiplier” of the function.
Hence here $f(x)=k(x+1)^2(x-1)^2$
$(-2,45)$ is on the graph thus $k\cdot(-1)^2(-3)^2=45\\9k=45\\k=5$
So $f(x)=5(x+1)^2(x-1)^2=5 x^4 - 10 x^2 + 5
$
