values of s along y axis

values of t along x axis

s=f(t)=a (t-p)(t-q)^2

where a, p, q are constants

the curve meets the coordinate axes at the points (0, -4.5) (1, 0) (3, 0)

find values for a, p ,q

i came up with three equations but they are so massive i doubt im on the right track.

i found

0 = a ( 27 - 18q + 3q^2 - 9p + 6pq - pq^2)

0 = a ( 1 - 2q + q^2 - p + 2pq - pq^2)

4.5 = apq^2

are these correct? if so, how can they be solved in a time period shorter than say a month?

somebody please show me step by step?