Final answer:
The transformation of the function g(x) from the parent function f(x) is a horizontal shift right by 1 unit and a vertical shift upwards by 2 units.
Step-by-step explanation:
The function g(x) = (x-1)^2+2 is a transformation of the function f(x) = x^2. The transformation can be described as a horizontal shift to the right by 1 unit, and a vertical shift upwards by 2 units. Since f(x) = x^2 represents a parabola opening upwards, applying the transformation makes f(x - 1) a horizontal shift to the right and +2 moves the graph upwards. This is a result of function translation principles. The graph of the function g(x) will be the same shape as f(x), but its vertex will be located at (1, 2) instead of the origin.