Answer:
121
Step-by-step explanation:
Given
f(x) = - (x + 8)(x - 14) ← expand factors using FOIL
= - (x² - 6x - 112) ← distribute by - 1
= - x² + 6x + 112
Given a quadratic in standard form. y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = - x² + 6x + 112 ← is in standard form
with a = - 1 and b = 6, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{6}{-2}[/tex] = 3
Substitute x = 3 into f(x) for corresponding value of y
f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121
vertex = (3, 121 ) ← with y = 121
