Question

which best describes the transformation that occurs from the graph of $f(x) = x^2$ to $g(x) = (x - 2)^2 + 3$?
○ right 2, up 3
○ left 2, down 3
○ right 2, down 3
○ left 2, up 3

Explanation:

Step1: Recall horizontal shift rule

For $f(x-h)$, shift right by $h$ units. Here $h=2$, so $f(x) \to f(x-2)$ shifts right 2.

Step2: Recall vertical shift rule

For $f(x)+k$, shift up by $k$ units. Here $k=3$, so $f(x-2) \to f(x-2)+3$ shifts up 3.

Answer:

right 2, up 3