Question

PLEASE HELP The function f(x) = x2 − 2x + 8 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

(1, 5)
(3, 7)
(1, 9)
(−1, 7)

Answer 1

Second one

Explanation:

Answer 2

Answer: Second option.

Explanation:

Given the function f(x):

`f(x) = x^2 - 2x + 8`

Find
`f(x -2)`:

`f(x -2)=(x-2)^2 - 2(x-2) + 8`

Remember that:

`(a\±b)^2=a^2\±2ab+b^2`

Then, simplifying:

`f(x -2)=x^2-2(x)(2)+2^2 - 2x+4+ 8\\\\f(x-2)=x^2-6x+16`

So the function g(x) is:

`g(x)=x^2-6x+16`

Use the following formula to find the x-coordinate of the vertex of g(x):

`x=(-b)/(2a)`

In this case:

`a=1\\b=-6`

Then:

`x=-(-(-6))/(2(1))=3`

Substitute this value into the function g(x) in order to find the y-coordinate of the vertex. Since
`g(x)=y`, you get:

`y=3^2-6(3)+16=7`

Therefore, the vertex of g(x) is:

`(3,7)`