To determine if the graph flips upward, we simply negate the absolute value.
y = | x + c | and y = | x - c | ------> upward
y = - | x + c | and y = - | x - c | ------> downward
To determine if the graph shifts to the right or left:
y = | x + c | ----> shifts to the left
y = | x - c | -----> shifts to the right
where c is a constant.
Keep in mind: the signs in front of the absolute value symbol does not matter in a shift.
Feel free to use a graphing calculator to experiment.