Find the values of a and k from the curve 
The diagram below shows a curve with equation of the form ${y = kx(x +
 a)^2}$, which passes through the points (-2, 0), (0, 0) and (1, 3).



What are the values of a and k.

I know my roots are x = -2, x = 0 and x = 3.
But as the y intercept is 0, I don't see how I can get any meaningful values for k:
${k(x + 2)(x - 3) = 0}$
How can I find the values of k and a?

x= -2 is a double root so, since you are told that it is a polynomial must have $(x- (-2))^2$ as a factor.
x= 0 is a root so f(0)= 0.
f(1)= 3.  
Further, this is clearly not a quadratic!  You are told that the function is of the form "$kx(x- a)^2$" not $k(x- 2)(x- 3)$.
The fact that x= -1 is a double root tells you what a is.  Then $k(1)(1- a)^2= 3$.
