Question

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

What is this function written in vertex form?


f(x) = (x –1)2 – 7

f(x) = (x +1)2 – 7

f(x) = (x –1)2 – 5

f(x) = (x +1)2 – 5

Answer 1

A is the correct answer i believe

Answer 2

Answer : A)
`f(x) = (x-1)^2 - 7`

Standard form of equation is
`f(x) = x^2 - 2x - 6`

The vertex form of equation is
`y= (x-h)^2 + k`

where (h,k) is the vertex

To find x coordinate of vertex we use formula
`h =(-b)/(2a)`

`f(x) = x^2 - 2x - 6`, a=1, b=-2 and c=-6

Plug in the values

`h =(-b)/(2a)=(-(-2))/(2*1)= 1`

Now plug in x=1 in the equation

`k =f(x) = 1^2 - 2(1) - 6 = 1-2-6= -7`

h= 1 and k=-7

The vertex form of equation is
`y= (x-h)^2 + k`

Plug in the values h=1 and k=-7

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