Question
\( f(x)=x^{2} \) \( g(x)=(x-9)^{2}+3 \) We can think of \( g \) as a translated (shifted) version of \( f \). Complete the description of the transformation. Use nonnegative numbers. To get the function \( g \), shift \( f \) up/down \( \vee \) by \( \square \) units and to the right/left \( \vee \) by \( \square \) units.
Ask by Bolton Gordon. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To get the function \( g \), shift \( f \) to the right by 9 units and upward by 3 units.
Solution
We start with f(x) = x². The function g(x) = (x - 9)² + 3 is obtained by making two changes to f(x):
1. Replace x with (x - 9), which shifts the graph of f(x) to the right by 9 units.
2. Add 3, which shifts the graph upward by 3 units.
So, to get the function g, shift f to the right by 9 units and upward by 3 units.
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Simplify this solution Beyond the Answer
To get the function \( g \), shift \( f \) up by \( 3 \) units and to the right by \( 9 \) units. This transformation takes the graph of \( f(x)=x^2 \), moves it \( 9 \) units to the right, and then \( 3 \) units up, resulting in the new vertex position of the parabola represented by \( g(x) \).
