Answer
$f(x) = (x^4 + x^3 - 3x^2 - x + 2)$
Work Step by Step
The zeros of this graph are at (-2, 0), (-1, 0) and (1,0).
At (1,0) , the graph "bounces" at that point, so that root is a zero with even multiplicity, so it will be to the power of two
Thus the polynomial will be $(x+2)(x+1)(x-1)^2$
$f(x) = (x^2 +3x + 2)(x^2 - 2x +1)$
$f(x) = (x^4 + x^3 - 3x^2 - x + 2)$
