f(x)=-2(x-2)squared-4 => f(x)=-2(x-2)^2 - 4 => 2(x^2-4x+4) - 4
This becomes f(x) = 2x^2 - 8x + 8 - 4.
This being a quadratic, a = 2, b = -8 and c = 4.
Theformula for the axis of symmetry is x = -b/(2a). Here, that comes to:
x = -(-8) / (2*2) = 8/4 = 2
The axis of symmetry here is the vertical line x = 2.