I'm not sure what you mean by that. It is true that, if n is even, (x- b)^n is never negative so that a(x- b)^n is never negative if a is positive and never positive if a is negative. Then (x- b)^n+ c is

1) equal to c at x= b and, if a>0, larger than c for x not equal to b.

2) equal to c at x= b and, if a< 0, less than c for x not equal to b.

In the first case, the graph goes down to a "vertex" at (a, c) and back up again.

In the second case, the graph goes up to a "vertex" at (a, c) and back down again.