Question

The image shows a geometric representation of the function f(x)=x^2-2x-6 written in standard form. What is the function written in vertex form?

Answer 1

y=(x-1)^2-7 This is this function in vertex form

Answer 2

`y=(x-1)^2-7`

Explanation:

Given : Equation =
`f(x)=x^2-2x-6`

To write in vertex form

Vertex form =
`y = a(x - h)^2+ k`

The given equation is in standard form
`y=x^2-2x-6`

to convert into vertex form we can use completing the square,

step 1 :
`y=x^2-2x-6`

step 2 :
`y+6=x^2-2x`

step 3 :
`y+6+1=x^2-2x+1`

step 4 :
`y+7=(x-1)^2`

step 5 :
`y=(x-1)^2-7`

It is a vertex form where a=1, h=1 , k=-7