Question

What is the vertex of the absolute value function defined by ƒ(x) = |x + 2| + 4?

(2,4)
(-2,-4)
(-2,4)
(2,-4)

Answer 1

Answer: C. (-2,4)

Explanation:

Answer 2

C. (-2,4)

Explanation:

We have been given a function
`f(x)=|x+2|+4` and we are asked to find the vertex of our absolute value function.

The rules for the translation of a function are as follows:

`f|x-h|=\text{Graph shifted to right by h units}`

`f|x+h|=\text{ Graph shifted to left by h units}`

`f|x|+h=\text{ Graph shifted upward by h units}`

`f|x|-h=\text{ Graph shifted down by h units}`

Upon comparing our absolute function with above transformations we can see that our function is shifted to two units right of the origin(0,0) so x coordinate of our absolute function will be -2.

Our function is shifted upward from origin by 4 units, therefore, y-coordinate of our absolute value function will be 4.

`f(x)=|x--2|+4`

Therefore, the vertex of our absolute value function will be on point (-2,4) and option C is the correct choice.