Question

the function $f(x) = x^2$ was transformed to create the function $g(x) = f(x - 3) - 9$. what are the coordinates of the vertex of the graph of $g$?
move the correct answer to each box. not all answers will be used.
$-9$ $-3$ $0$ $3$ $9$
$(\\_\\_\\_\\_\\_\\_,\\_\\_\\_\\_\\_\\_)$

Explanation:

Step1: Identify vertex of $f(x)$

The vertex of $f(x)=x^2$ is $(0,0)$.

Step2: Apply horizontal shift

For $f(x-3)$, shift vertex right 3: $(0+3, 0)=(3,0)$.

Step3: Apply vertical shift

For $f(x-3)-9$, shift vertex down 9: $(3, 0-9)=(3,-9)$.

Answer:

$\boldsymbol{(3, -9)}$