The equation of the polynomial graphed is
f(x) = 1/3(x + 3)(x - 1)(x - 2)
How to find the equation
The equation of the polynomial is solved using the formula
f (x) = a (x - p) (x - q) (x - r).....
Where p, q, r, ... are the roots of the equation
From the graph the roots are x = -3, x = 1 and x = 2
In factored form we have
f (x) = a (x + 3) (x - 1) (x - 2)
To solve for a we use point (0, 2)
2 = a (0 + 3) (0 - 1) (0 - 2)
2 = a * 3 * -1 * -2
2 = 6a
a = 1/3
So the equation of the polynomial is
f(x) = 1/3(x + 3)(x - 1)(x - 2)