y = |x| is a v-shaped graph that opens up and have vertex (0, 0).
Now we need to see each change done to it.
y = -|x| makes every y-coordinate its additive inverse, so y = -|x| still has the vertex at (0, 0), but now is turned downward.
y = -|x| + 2 can be changed to
y - 2 = -|x|
Now y was replaced by y - 2. When y is replaced by y - k, the graph shifts vertically k units. In this case, k = 2, so the graph shifts up 2 units. The vertex is now at (0, 2).
Vertex: (0, 2)
Domain: all real numbers
Range: all real numbers less than or equal to 2.
