5
advanced-math

If a parabola opens downward and has a vertex at (2,5)(2, 5), how many x-intercepts does it have?

A

2

B

1

C

0

D

Cannot be determined

Correct Answer: A

Choice A is the correct answer.

  1. Vertex: (2,5)(2, 5) is above the x-axis (y is positive).
  2. Direction: Opens downward.
  3. Conclusion: Since it starts above the axis and goes down, it must cross the x-axis twice.

Choice B is incorrect because that requires vertex on x-axis. Choice C is incorrect because that requires vertex below x-axis (for downward). Choice D is incorrect because the geometry is fixed.

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Set 9: Quadratic Equations and Functions 9