Curve equation?

Question

The curve with equation y = x^2 has been translated to give the curve y = f(x).

Find f(x) in terms of x.

Please go step by step and explain well.

Answer 1

In a translation the coordinates of a point
(x,y) become (X,Y) with
X= x-xo and Y= y-yo where (xo,yo) are the old coordinates of the new origin.
So y=x^2 becomes
Y+yo = (X-xo)^2