If the parent function is f (x) = x^2 and its transformed fuction is g (x) = 2 (x-1) ^2

Given:

f (x) = x², the parent function

g (x) = 2 (x-1) ²

The transformations required are

1. Shift f (x) right by 1 unit to obtain

(x-1) ²

2. Magnify (dilate) by a factor of 2 to obtain

2 (x-1) ²

Answer: A right shift by 1, and magnification (dilation) of 2.