Question

What is the vertex of the absolute value function defined by ƒ(x) = |x - 2| - 7?

Answer 1

The vertex is (h, k) just like in other functions.
The h is 'inside' the absolute value bars and the k is 'outside' the absolute value bars.
The function is:
f(x) = a | x - h | + k
a changes the shape, h moves the graph left/right, and k moves the graph up/down.
f(x) = | x - 2 | - 7
Vertex (2, - 7)

Answer 2

The correct answer is (2,-7)