Question

What is the transformations needed to obtain `f(x)= (x-2)^2` from the graph of `x^2`?

Answer 1

`x^2` shifted -2 units on the `x`-axis `=f(x)`

Explanation:

If `g(x)=x^2`and `f(x)=(x-2)^2`
then `f(x)=g(x-2)`

Hence the transformation needed to obtain `f(x)` from `g(x)` is a shift of -2 units on the `x`-axis.

This can be seen on the graphs of `g(x)` and f(x) below:

graph{x^2 [-5.69, 5.41, -1.44, 4.11]}

graph{(x+2)^2 [-5.69, 5.41, -1.44, 4.11]}