I am confused on how to solve this problem.

Question

f(x)=a(x+b)(x-8)

The equation above represents a quadratic function where a and b are constants. If the function is graphed in the xy-plane, its vertex is at the point (2, -54). What is the value a and b?

Answer 1

a= 1.5, b= 4

y=a(x+b)(x-8) x intercepts are 8 and -b, their midpoint is the x coordinate of the vertex =2

(8-b)/2 = 2

8-b = 4

b = 4

plug in the vertex to calculate a

-54 =a(2+4)(2-8) = -36a

a = 54/36 = 3/2