Question

Question 6(Multiple Choice Worth 1 points)

(08.05 MC)
The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x - 2). Find the vertex of g
(-1,-8)
(-3,-4)
(-1,-6)
(-5-6)​

Answer 1

(-1,-6)

Explanation:

We have the following function:

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

The following transformation is applied

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

So

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

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

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

For a second order function in the format:

`g(x) = ax^(2) + bx + c`

The vertex is:

`V = (x_(v), g(x_(v))`

In which

`x_(v) = -(b)/(2a)`

In this problem

`a = 1, b = 2`

So

`x_(v) = -(2)/(2*1) = -1`

Then

`g(x_(v)}) = g(-1) = (-1)^(2) +2(-1) - 5 =  -6`

So the correct answer is:

(-1,-6)