Advanced MathHardReading a parabola in vertex form
Advanced Math practice question
The function h is defined by h(x) = −(x − 3)² + 9. Which of the following is true about the graph of h in the xy-plane?
- A. Its maximum value is 9, at x = 3.Correct
- B. Its minimum value is 9, at x = 3.
- C. Its maximum value is 3, at x = 9.
- D. It passes through (3, 0).
Answer: A. Its maximum value is 9, at x = 3.
The negative sign opens the parabola downward, and the vertex (3, 9) is its highest point.
Why the other answers are wrong
- B. Its minimum value is 9, at x = 3.
- A downward parabola has a maximum, not a minimum.
- C. Its maximum value is 3, at x = 9.
- The coordinates are swapped.
- D. It passes through (3, 0).
- h(3) = 9, not 0.
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