Question

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

Answer 1

Answer: d. 121 on edgen2021

Explanation:

Answer 2

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`