P(x) is symmetrical to the y-axis ... that should tell you what the coefficients "a" and "c" are.

max at (0,1) tells you two things ... the value of "d" and that P'(x) = 0

abs min at (q, -3) is also at (-q, -3) ... graph is symmetrical.

also, P'(x) = 0 at x = q and x = -q.

work on it.