A quadratic function with equation:

f(x) = ax^2/2 + bx + c

Passes through the points

(0,2) and (2,-6)

And has a gradient of 1 at x=3.

Solve for the constants a, b and c.

I have c, which is 2, however i have no idea how to find the others.

I understand differentiation and know how to do it etc, i am just not sure about how to apply it to this question/ do the simultaneous equations required.

Just for reference, the answers are :

A = 5/2

B= -13/2

C= 2