The general equation of a parabola with the vertex shifted k units horizonatally is given by,
[tex]g(x)=(x-k)^2[/tex]If k is positive, the graph is shifted k units to the right and if k is negative, the graph is shifted k units to the left.
If a graph is shifted 2 units to the right, then k=2.
So, if
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=(x-k)^2=(x-2)^2 \end{gathered}[/tex]Hence, option C is correct.
