Answer:
49
Step-by-step explanation:
Given
f(x) = - (x - 3)(x + 11)
Find the zeros by setting 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
The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros
[tex]x_{vertex}[/tex] = [tex]\frac{3-11}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4
Substitute x = - 4 into f(x) for y- coordinate of vertex
f(- 4) = -(- 7)(7) = 49 ← y- value of vertex
