Question

The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.

Answer 1

we know that

To find the equation in vertex form, we need to factor the function

so

$f(x) = x^{2} - 2x - 6$

Complete the square. Remember to balance the equation

$f(x) = x^{2} - 2x +1-1- 6$

$f(x) = x^{2} - 2x +1-7$

Rewrite as perfect squares

$f(x) = (x-1)^{2} -7$

in this problem

the vertex is the point $(1,-7)$

therefore

the answer is

The function written in vertex form is equal to $f(x) = (x-1)^{2} -7$