# How do you graph y>=abs(x-1)-2?

Feb 16, 2018

This is an absolute value inequality, so it's going to have a V shape.

#### Explanation:

The -1 inside the absolute value will shift it RIGHT by one unit. It may seem like you'd shift it left, but that is incorrect.

The -2 will shift it down 2 units.

So, the vertex will be at (1,-2)

Then, for the inequality, I like to use the origin (0,0) for my test point. Substitute 0 for both x and y in the inequality.

That gives $0 \ge \left\mid - 1 \right\mid - 2 \to 0 \ge 1 - 2 \to 0 \ge - 1$

Then, you need to determine if 0 is greater than or equal to -1. Since it is, that means the point (0,0) will be included in your shading.