Advanced MathEasy–MediumTrue statement about a parabola in vertex form
Advanced Math practice question
Which of the following statements is true about the graph of f(x) = (x − 2)² + 3 in the xy-plane?
- A. Its minimum value occurs at the point (2, 3).Correct
- B. Its maximum value occurs at the point (2, 3).
- C. It crosses the x-axis at x = 2.
- D. Its y-intercept is 3.
Answer: A. Its minimum value occurs at the point (2, 3).
(x − 2)² is never negative, so f is smallest, 3, at x = 2: a minimum at (2, 3).
Why the other answers are wrong
- B. Its maximum value occurs at the point (2, 3).
- The parabola opens upward, so the vertex is a minimum.
- C. It crosses the x-axis at x = 2.
- f(2) = 3, not 0; the graph never reaches the x-axis.
- D. Its y-intercept is 3.
- f(0) = 4 + 3 = 7.
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