Calculus Problem Solving Question

[danizh]

Please help me solve this problem.

Find numbers a, b, and c so that the graph of f(x) = ax^2 + bx + c has x-intercepts at (0,0) and (8,0) and a tangent with slope 16 where x = 2.

I have done this so far:
f(x) = ax^2 + bx + c
f '(x) = (2)(a)(x) + b
16 = (2)(a)(2) + b
16 = 4a + b

I don't know where to go from here, so any help would be greatly appreciated.

 

[danizh]

Nevermind, I solved it. If anyone else needs the solution to this problem, let me know. :)