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:

For a quadratic function in the form $g(x) = (x - h)^2 + k$ derived from the parent function $f(x) = x^2$:

1. The value of $h$ determines horizontal shift: if $h>0$, the graph shifts right by $h$ units. Here $h=2$, so shift right 2.
2. The value of $k$ determines vertical shift: if $k>0$, the graph shifts up by $k$ units. Here $k=3$, so shift up 3.

This matches the visual shift of the parabola in the graph.

Answer:

right 2, up 3