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