Advanced MathEasy–MediumReading a parabola's vertex
Advanced Math practice question
In the xy-plane, the graph of y = f(x) is a parabola that opens upward with its vertex at (2, −3). Which of the following statements is true?
- A. The minimum value of f is −3, and it occurs at x = 2.Correct
- B. The maximum value of f is −3.
- C. The equation f(x) = 0 has no real solutions.
- D. f(−3) = 2
Answer: A. The minimum value of f is −3, and it occurs at x = 2.
An upward parabola's vertex is its lowest point.
Why the other answers are wrong
- B. The maximum value of f is −3.
- An upward parabola has no maximum.
- C. The equation f(x) = 0 has no real solutions.
- The vertex is below the x-axis and the graph rises, so it crosses the axis twice.
- D. f(−3) = 2
- The vertex gives f(2) = −3, not f(−3) = 2.
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