Question

Which best describes he transformation that occurs

from the graph of f(x) = x2 to g(x) = (x - 2)2 = 32 A) Right 2, up 3
B) Left 2, down 3
C) Right 2, down 3
D) Left 2, up 3

Answer 1

The correct transformation from f(x) to g(x) is a horizontal shift to the right by 2 units and a vertical shift upwards by 3 units, which corresponds to Option A: Right 2, up 3.

Step-by-step explanation:

The transformation that occurs from the graph of f(x) = x² to g(x) = (x - 2)² + 3 involves a shift to the right by 2 units and an upward shift by 3 units. This is because the (x - 2) part of the equation indicates a horizontal transformation moving the vertex of the parabola to the right from the origin (0,0) to (2,0), which is horizontal movement. The +3 indicates a vertical transformation, moving the graph upwards by 3 units. Thus, the correct transformation description is Option A: Right 2, up 3.