Question

The graph of which inequality has its vertex at (2 1/2, 5)?

The correct answer to this is y>|2x-5|+5.
My question is where did the 2 1/2 come from in the vertex?

Answer 1

77777

Explanation:

Answer 2

In this case, the vertex is the lowest point of the V shaped curve.

The goal is to get the stuff inside the absolute value (the 2x-5) to be as small as possible, so we can get to the lowest point. In terms of absolute value, we want the 2x-5 to be equal to 0

This allows us to set up the equation below and solve for x.

2x-5 = 0

2x = 5

x = 5/2

x = (4+1)/2

x = 4/2 + 1/2

x = 2 + 1/2

x = 2 & 1/2

Let me know if this clears things up or not.