Answer:
49
Step-by-step explanation:
The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros.
Find the zeros by letting f(x) = 0, that is
- (x - 3)(x + 11) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 11 = 0 ⇒ x = - 11, thus
[tex]x_{vertex}[/tex] = [tex]\frac{-11+3}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4
Substitute x = - 4 into f(x) for y- value of the vertex
f(- 4) = - (- 4 - 3)(- 4 + 11) = - (- 7)(7) = 49
