f(x)=|x+2|-3 The maximum point is -3 because that is the vertical shift.
f(x)=-|x-2|-3 The minimum point is -3 because that is the vertical shift.
As for the problem in the picture, the vertex is (5,3) because you take the opposite in the absolute value sign and you leave the vertical shift the same, and the graph is shifted 5 units right and 3 units up (Knowing this shift can help you figure out the vertex). The graph opens downward because there is a negative sign in front of it. The maximum is 3 because that is the vertical shift.