If I have y=x^2 then to shift by 1 on x axis I just do this: (x-1)^2

But due to constant expression I am a bit confused.

The only way I can see to do this is to factorise and then shift factors 1 to the right.

Eg factors of x^2 -2x -3 are (x+1)(x-3) to transform by 1 just add one to each factor: ie becomes x(x-4) - then expand out to x^2 -4x.

Is that the easiest way to do it?

Just checking I am using the best technique.

Angus