Respuesta :
The function in vertex form that is equivalent to the equation f(x) = x^2 + 8 - 16x from the given options is given by: Option A: f(x) = (x-8)^2 -56
What is vertex form of a quadratic equation?
If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
Since it is specified that the options are in vertex form, so let we convert the given equation to vertex form.
The specified equation is: [tex]f(x) = x^2 + 8 - 16x[/tex]
Converting to vertex form:
[tex]f(x) = x^2 + 8 - 16x\\\\f(x) = x^2 -16x + 8\\[/tex]
(let we make terms such that it becomes (a+b)^2 's formula).
[tex]f(x) = x^2 -16x + 8\\f(x) = x^2 -2\times8x + (-8)^2 -(-8)^2 + 8\\f(x) = (x-8)^2 -64 + 8\\f(x) = (x-8)^2 -56[/tex]
Thus, the function in vertex form that is equivalent to the equation f(x) = x^2 + 8 - 16x from the given options is given by: Option A: f(x) = (x-8)^2 -56
Learn more about vertex form of a quadratic equation here:
https://brainly.com/question/9912128
