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 $h$ units.
Here, $g(x)=(x-2)^2+3$ has $h=2$, so shift $f(x)=x^2$ right 2.

Step2: Recall vertical shift rule

For $f(x)+k$, shift up $k$ units.
Here, $g(x)=(x-2)^2+3$ has $k=3$, so shift up 3.

Answer:

right 2, up 3