Use the equation and its derivative to build a system of equations. It should be rather simplistic.

The max and min occur at (0,0) and (2,4)

We have:

, therefore, d=0.

Derivatives must be 0 at extrema:

, therefore, c=0.

Because c and d are 0, that helps whittle things down a good bit.

We have the following system to solve:

We find a=-1 and b=3

Therefore, the polynomial is