Question

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

Answer 1

The vertex form of the equation of a parabole is (x - h)^2 + k

So you must complete squares to transform x^2 -2x - 6 in its vertex form.


1) convert x^2 - 2x in a square => (x - 1)^2 - 1

2) Add the constant term - 6 => (x - 1)^2 -1 - 6

3) Add similar terms => (x - 1)^2 - 7

You can verify that (x - 1)^2 - 7 is equal to x^2 - 2x - 6:

x^2 - 2x + 1 - 7 = x^2 - 2x - 6. So, do not doubt it, the vertex form is (x - 1)^2  - 7, where the coordinates of the vertex are (1, - 7)

Answer: option A (x - 1)^2 - 7