Consider the absolute vale function f(x)=-|x+2|-2the vertex of the function is

The vertex of the absolute value function f(x) = |x| is (0,0).
What about f(x)=-|x+2|-2?  This can be re-written as f(x) = -|x-(-2)| -2.
Three things happen here:  first, the graph of f(x) = |x| must be inverted, so that it opens down instead of up; second, the resulting graph must be translated 2 units to the left; and third, the resulting graph must be translated 2 units down.