How to move the position of a curve $x,y$ coordinates?

Question

I have some silly problem. I want to know how to move the curve in $x,y$ coordinates which I have some curve.

For example, $f(x) = x^2$ and this is originally start at $(0,0)$. But I want to this curve is start at $(3,2)$. Then How do I make modify the equation?

Answer 1

If you mean that you want to shift the minimum to $(3,2)$, then your function will be $(x-3)^{2}+2$. First, you move the curves 3 units to the right, and 2 upwards.

Answer 2

To move origin of coordinates to $(x_0,y_0)$ point just replace $(x,y)$ by $(x-x_0,y-y_0)$ in your $y = f(x)$ equation.

Answer 3

If you want to move the origin of coordinates from $(0,0)$ to $(h,k)$,just replace original coordinates by $(x-h,y-k)$ in original equation.