1. Graph the solution to the inequality y ≤ -2(x - 2)2 - 2 ?

Answer 1

I am sure you meant:
y ≤ -2(x - 2)^2 - 2
which would be everything below and including the parabola, which itself opens downwards and has a vertex of (2,-2)

http://www.wolframalpha.com/input/?i=y+%E2%89%A4+-2%28x+-+2%29%5E2+-+2