To determine if the vertex of y=-2(x-2)^2-2 is a negative value or a positive one, we find the second derivative of y and see if it is positive or negative. If the second derivative at the vertex if positive it is a minimum value, else it is a maximum value.
y = -2*x^2 - 2
=> y' = -4x
=> y'' = -4
This gives that the value at the vertex is a maximum.
We know that if leading coefficient of the quadratic is positive, than the parabola has a minimum point, this one being the vertex of the parabola.
a is the leading coefficient
If the leading coefficient is negative, than the vertex represents a maximum point.
We can notice that the leading coefficient is negative, a=-2, so the parabola has a maximum point.