Question

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

Answer 1

something funny is that the x value of the vertex lies directl in the middle of the x intercepts
so
we see the x intercepts or 0's at x=8 and 2
the average is x=5
so find f(5) to find the y value of the vertex
f(5)=(5-8)(5-2)
f(5)=(-3)(3)
f(5)=-9

vertex is at (5,-9)

the actual way the teacher wants is to expand then compltete the square to get into the form f(x)=a(x-h)^2+k where the vertex is (h,k)
but whatever


verrtex is at (5,-9)

Answer 2

The vertex of the function is (5,-9)

The equation is given as:

$f(x) = (x - 8)(x - 2)$

Expand

$f(x) = x^2 - 8x -2x + 16$

Simplify

$f(x) = x^2 - 10x + 16$

Factorize

$f'(x) = 2x - 10$

Set to 0

$2x - 10 = 0$

Solve for x

$x = 5$

Calculate f(5)

$f(5) = (5 - 8)* (5 -2)$

$f(5) = -9$

Hence, the vertex of the function is (5,-9)

Read more about quadratic functions at:

https://brainly.com/question/1214333