Question

What is the y-value of the vertex of the function f(x) = –(x – 3)(x + 11)?

Answer 1

the y-value of the vertex is 49

Answer 2

y- value of the vertex for the given function
`\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)` is 49.

Explanation:

Given : The function
`\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)`

We have to find the y- value of the vertex for the given function.

Consider the given function
`\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)`

The vertex of the up-down facing parabola of the form
`y=a\left(x-m\right)\left(x-n\right)` is the average of the zeros,
`x_v=(m+n)/(2)`

Thus, here, m = 3 , n = -11 and a = 1

`x_v=(3+\left(-11\right))/(2)=-4`

Thus, x- value of vertex is -4.

Now, put x = -4 to get y values

`y_v=-\left(-4-3\right)\left(-4+11\right)=49`

Thus, y- value of the vertex for the given function
`\:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)` is 49.