Advanced MathEasy–MediumEquation of a shifted parabola
Advanced Math practice question
The graph of y = x² in the xy-plane is shifted 2 units to the left and 5 units down. Which of the following is an equation of the resulting graph?
- A. y = (x + 2)² − 5Correct
- B. y = (x − 2)² − 5
- C. y = (x + 2)² + 5
- D. y = (x − 2)² + 5
Answer: A. y = (x + 2)² − 5
A shift left replaces x with x + 2; a shift down subtracts 5.
Why the other answers are wrong
- B. y = (x − 2)² − 5
- x − 2 shifts the graph right.
- C. y = (x + 2)² + 5
- +5 shifts the graph up.
- D. y = (x − 2)² + 5
- Both directions are reversed.
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