The graph of y = x2-1 without the absolute value is:

 

The graph of y = |x2-1| (with the absolute value
is:



The part to the left of -1, which is x < 1 and the parts to the right
of  1, which is x > 1 are the same as y = x2-1.  

The part between -1 and 1, which is -1 < x < 1 is the reflection of 
y = x2-1 across the x axis, which multiplies it by -1, or  y = -x2+1.

So the "break" points are at  -1 and 1.

Since the graph is continuous at the "break" points, it doesn't
matter whether you put them as part of the part to the left or
the part to the right,  So any of these is correct:


 






Or, an even shorter way is to combine
the 1st and 3rd parts, since they are both 
x2-1,



or



All of these are correct.

Edwin