Question

which best describes the transformation that occurs from the graph of $f(x) = x^2$ to $g(x) = (x + 3)^2 + 4$?\
\bigcirc\\; left 3, up 4\
\bigcirc\\; right 3, down 4\
\bigcirc\\; left 3, down 4\
\bigcirc\\; right 3, up 4

Explanation:

Step1: Recall horizontal shift rule

For $f(x-h)$, $h>0$ shifts right $h$, $h<0$ shifts left $|h|$. Here $g(x)=(x+3)^2+4=(x-(-3))^2+4$, so $h=-3$, shift left 3.

Step2: Recall vertical shift rule

For $f(x)+k$, $k>0$ shifts up $k$, $k<0$ shifts down $|k|$. Here $k=4$, shift up 4.

Answer:

left 3, up 4