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

Answer:

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

Step-by-step 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, $x_v=\frac{m+n}{2}$

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

$x_v=\frac{3+\left(-11\right)}{2}=-4$

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.