The vertex of a function is the minimum of the maximum of the function
The function in vertex form is [tex]f(x) = (x - 8)^2 - 56[/tex]
The function is given as:
[tex]f(x) = x^2 + 8 - 16x[/tex]
Rewrite the equation as:
[tex]f(x) = x^2 - 16x+ 8[/tex]
Let k represent the coefficient of x.
[tex]k = -16[/tex]
Divide both sides by 2
[tex]k/2 = -8[/tex]
Take the square of both sides
[tex](k/2)^2 = 64[/tex]
So, we have:
[tex]f(x) = x^2 - 16x+ 8[/tex]
[tex]f(x) = x^2 - 16x + 64 - 64 + 8[/tex]
[tex]f(x) = x^2 - 16x + 64 - 56[/tex]
Rewrite as:
[tex]f(x) = [x^2 - 16x + 64] - 56[/tex]
Express as a perfect square equation
[tex]f(x) = (x - 8)^2 - 56[/tex]
Hence, the function in vertex form is [tex]f(x) = (x - 8)^2 - 56[/tex]
Read more about vertex form at:
https://brainly.com/question/15914313
