Question

The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

Answer 1

(-5,-6)

Explanation:

just took the test and got it right

Answer 2

(-1,-6)

Explanation:

`f(x)=x^2+6x+3`

`g(x)=f(x-2)`

`g(x)=(x-2)^2+6(x-2)+3` (Replaced x in f with (x-2))

`g(x)=x^2-4x+4+6x-12+3` (Used
`(x+b)^2=x^2+2bx+b^2` and distributive property)

`g(x)=x^2-4x+6x+4-12+3` (Gathered like terms)

`g(x)=x^2+2x-5` (Simplified)

The vertex of a parabola occurs at
`((-b)/(2a),g((-b)/(2a))`.

Let's find
`(-b)/(2a)` first.

`(-2)/(2(1))=-1`

Now we can obtain
`g((-b)/(2a))` which is
`g(-1)` in this case:

`g(x)=x^2+2x-5`

`g(-1)=(-1)^2+2(-1)-5`

`g(-1)=1-2-5`

`g(-1)=-1-5`

`g(-1)=-6`.

The vertex is (-1,-6).