The y-value of the vertex of the function is 121.
Given
The function is;
[tex]\rm f(x)=-(x +8)(x-14)[/tex]
The vertex of the parabola of a quadratic function is given by;
[tex]\rm \text{The vertex of the parabola}= \dfrac{-b}{2a}[/tex]
Expand the function then solve;
[tex]\rm f(x)=-(x +8)(x-14)\\\\f(x)=-(x(x-14)+8(x-14))\\\\f(x)=-(x^2-14x+8x-112)\\\\f(x)= -x^2+6x+112[/tex]
The y-value of the vertex of the function is;
[tex]\rm \text{The vertex of the parabola}= \dfrac{-b}{2a}\\\\\rm \text{The vertex of the parabola}= \dfrac{-6}{2\times -1}\\\\\rm \text{The vertex of the parabola}= 3[/tex]
Substitute x = 3 into f(x) for corresponding value of y
f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121
Hence, the y-value of the vertex of the function is 121.
To know more about the vertex of the parabola click the link given below.
https://brainly.com/question/595002
