Question

What is the vertex of the graph of y = |2x - 6| - 4?
A. (3, -4)
B. (-3, -4)
C. (2, -4)
D. (6, -4)

Answer 1

By definition of |x|,

|2x-6|-4 = {2x-6-4 = 2x-10 if 2x-6≥0
{-(2x-6)-4 = 2-2x if 2x-6<0

So , the graph is composed of two lines, one with positive slope and other with negative slope.

So the vertex must be the instersection point between those lines.
So the x coordinate of that point, is given by the equation

2x-10 = 2-2x

Solving for x and y, the answer happens to be (3,-4)