y=ax^4 + bx^3 + cx^2 + dx + e
Since a< 0 we know that it has to go to - infinity for x going to - infinity and x going to + infinity. That rules out choices B and C.
The maximum number of turning points a polynomial can have is n-1 where n is the degree of the polynomial
(turning points is change of direction)
The graph D has 5 turning points and the degree of the polynomial is 4 so it is not possible
A is your solution.