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

Step2: Recall vertical shift rule

For $f(x)=x^2+k$, $k>0$ shifts up $k$.
Here $k=4$, so shift up 4.

Answer:

left 3, up 4