The corner of an absolute value function represents a turning point in the graph where the function decides to apply a certain “action” to an interval.
In an absolute value function, setting the inner function equal to zero is a way of indirectly checking the intervals that either initiate -(x+-a) for x < a or x+-a for x>=a, i.e., checking the x values that make the inner function equate to a number greater than zero (those values would use x+-a, x>=a) or making the inner function less than or equal to zero (those value would use -(x+-a), x.