ANSWER
D.
[tex]f(x) = - {x}^{4} + {x}^{3} + 3 {x}^{2} [/tex]
EXPLANATION
The given graph rises on the left and falls on the right.
This implies that the degree of the function is even.
Since the graph opens downward, the coefficient of the leading term must be negative.
The graph graph of the function also has 3 intercepts with one of them having an even multiplicity.
This means that the degree must be 4.
Therefore the last choice is correct.
