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)
, 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