Question 2 (1 point)
Compared to the graph of the base function $y=x^{2}$, the graph of the function $g(x)=(x-9)^{2}+4$ is translated
\[\boxed{\text{The graph of the function } g(x)=(x-9)^{2}+4 \text{ is translated 9 units to the right and 4 units up compared to the graph of the base function } y=x^{2}.}\]
Step 1 :The function $g(x)=(x-9)^{2}+4$ is a transformation of the base function $y=x^{2}$. The transformation involves a horizontal shift and a vertical shift.
Step 2 :The term $(x-9)$ in the function $g(x)$ indicates a horizontal shift of 9 units to the right.
Step 3 :The term $+4$ indicates a vertical shift of 4 units upwards.
Step 4 :Therefore, compared to the graph of the base function $y=x^{2}$, the graph of the function $g(x)=(x-9)^{2}+4$ is translated 9 units to the right and 4 units up.
Step 5 :\[\boxed{\text{The graph of the function } g(x)=(x-9)^{2}+4 \text{ is translated 9 units to the right and 4 units up compared to the graph of the base function } y=x^{2}.}\]