The graph of y = ax2 + bx + c is a parabola that opens up and has a vertex at (-2, 5). What is the solution set of the related equation 0 = ax2 + bx + c?

Question

tad1 · Answer

-2 = -b/2a. Therefore b = 4a.
Substitute into 5 = 4a -2b +c and it becomes -b + c = 5.
We also have the equation 0 = 2ax + bx + c = x(2a + b) + c = x((3/2b)x + c
So we have a system of two equations in two unknowns which can be solved and then back-substituted to find a.  I'm sure there's a cleaner way to do this problem, but this way works.