Answer:
C. (-2,4)
Step-by-step explanation:
We have been given a function [tex]f(x)=|x+2|+4[/tex] and we are asked to find the vertex of our absolute value function.
The rules for the translation of a function are as follows:
[tex]f|x-h|=\text{Graph shifted to right by h units}[/tex]
[tex]f|x+h|=\text{ Graph shifted to left by h units}[/tex]
[tex]f|x|+h=\text{ Graph shifted upward by h units}[/tex]
[tex]f|x|-h=\text{ Graph shifted down by h units}[/tex]
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.
[tex]f(x)=|x--2|+4[/tex]
Therefore, the vertex of our absolute value function will be on point (-2,4) and option C is the correct choice.
