Question

What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?

Answer 1

we have

$f(x)=-(x+8)(x-14)$

Convert to vertex form

$f(x)=-(x+8)(x-14)\\f(x)=-( x^{2}-14x+8x-112) \\f(x)=-( x^{2}-6x-112)\\f(x)=-x^{2}+6x+112$

we know that

the equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

$f(x)=-x^{2}+6x+112$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-112=-(x^{2}-6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-112-9=-(x^{2}-6x+9)$

$f(x)-121=-(x^{2}-6x+9)$

Rewrite as perfect squares

$f(x)-121=-(x-3)^{2}$

$f(x)=-(x-3)^{2}+121$

the vertex is the point $(3,121)$

therefore

the answer is

The y-value of the vertex is $121$