The graph of the quadratic function y = ax^2 + bx + c opens downwards and its vertex is at (2, -3). Which of the following statements must be true?

A a > 0

B c > 0

C b > 0

D a < 0

✓ Correct Answer: Option D

For a quadratic function y = ax^2 + bx + c, the parabola opens downwards if and only if the leading coefficient 'a' is negative (a < 0).

💡 Why is D) the correct answer?

The correct answer to the question "The graph of the quadratic function y = ax^2 + bx + c opens downwards and its vertex is at (2, -3). Which of the following statements must be true?" is Option D: a < 0.

The other options — A) a > 0, B) c > 0, C) b > 0 — are incorrect for this GRE Exam Prep question. As explained above: For a quadratic function y = ax^2 + bx + c, the parabola opens downwards if and only if the leading coefficient 'a' is negative (a < 0).

📚 About This GRE Exam Prep Practice Question

This 2-level GRE Exam Prep question from the Quantitative Reasoning topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free GRE Exam Prep practice test or use flashcards for spaced repetition review.

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The graph of the quadratic function y = ax^2 + bx + c opens downwards and its vertex is at (2, -3). Which of the following statements must be true?

✓ Correct Answer: Option D

📚 About This GRE Exam Prep Practice Question

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