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

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 Link

MrRoyal MrRoyal · Answer 2 · 2022-03-25T17:04:17+01:00

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

The equation is given as:

[tex]f(x) = (x - 8)(x - 2)[/tex]

Expand

[tex]f(x) = x^2 - 8x -2x + 16[/tex]

Simplify

[tex]f(x) = x^2 - 10x + 16[/tex]

Factorize

[tex]f'(x) = 2x - 10[/tex]

Set to 0

[tex]2x - 10 = 0[/tex]

Solve for x

[tex]x = 5[/tex]

Calculate f(5)

[tex]f(5) = (5 - 8)* (5 -2)[/tex]

[tex]f(5) = -9[/tex]

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

Read more about quadratic functions at:

https://brainly.com/question/1214333