When you say that f(2+x)=f(2-x) means that the symmetry axis is x=2, f(a)=f(b), (a, b are algebraic expressions with x), then x=(a+b)/2 is the symmetry axis.

What you want to ask may be f(x)=-f(x+2), so a half cycle like this is 2, mainly using the idea of substitution.