Let x = 5 (for illustration. x will remain 5 for the whole exercise)
f(x) = - x^2
f(x) is a function which takes any value (x), squares it, then negates it.
So, if x = 5, f(5) = - x^2 = -25
In this case, x-2 is 5-2 = 3, so f(3) = -9
So f(x-2) = -9
And y = -(x-2)^2 = - (5-2)^2 = -(3)^2 = -9
So f(x-2) = y = -(x-2)^2
But put simpler, you can substitute anything for x
If you change f(x) to f(x-2), then - x ^2 becomes - (x-2)^2, which is y.
And it even works without colours!