Advanced MathHardTranslating a parabola
Advanced Math practice question
The graph of the function g in the xy-plane is the graph of f(x) = x² shifted 3 units to the right and 2 units down. Which equation defines g?
- A. g(x) = (x − 3)² − 2Correct
- B. g(x) = (x + 3)² − 2
- C. g(x) = (x − 3)² + 2
- D. g(x) = (x − 2)² − 3
Answer: A. g(x) = (x − 3)² − 2
A shift RIGHT by 3 replaces x with (x − 3); a shift DOWN by 2 subtracts 2 from the output. So g(x) = (x − 3)² − 2, with vertex at (3, −2).
Why the other answers are wrong
- B. g(x) = (x + 3)² − 2
- (x + 3)² shifts the graph 3 units to the LEFT. Right shifts subtract inside the parentheses.
- C. g(x) = (x − 3)² + 2
- +2 outside shifts the graph UP. A downward shift subtracts.
- D. g(x) = (x − 2)² − 3
- This swaps the two shifts: it moves 2 right and 3 down.
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