G(x) is obtained from F(x) after both horizontal and vertical translation.
Following translations occur in F(x) to obtain G(x)
a) 2 units to Right
b) 4 units down
Translation towards right can be expressed as:
F(x - 2)
Vertically down translation can be expressed as:
F(x-2) - 4
So,
G(x) = (x-2)² - 4
Thus, option A is the correct answer.