Problem

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

Answer

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Answer

\[\boxed{\text{The graph of the function } g(x)=(x-9)^{2}+4 \text{ is translated 9 units to the right and 4 units up compared to the graph of the base function } y=x^{2}.}\]

Steps

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 :\[\boxed{\text{The graph of the function } g(x)=(x-9)^{2}+4 \text{ is translated 9 units to the right and 4 units up compared to the graph of the base function } y=x^{2}.}\]

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