Exam-style question
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B3: Explain how to approach quadratic functions and their graphs in an AQA A-level Mathematics question. Your answer should identify the method, the key notation and one check on the final result.
Model answer
What a good answer should say
- Use the discriminant when the question asks about the number or type of roots.
- Calculate b^2 - 4ac and interpret its sign: positive means two real roots, zero means a repeated root, and negative means no real roots.
- This is different from simply solving the quadratic, because the discriminant gives root information without requiring the roots themselves.
- A common mistake is forgetting that repeated roots occur exactly when the discriminant is zero.
This answer is tied to the objective: B3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown..
Explanation
Why this works
Use the explanation to connect the worked answer back to B3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown..
This B3 response focuses on discriminant reasoning and root classification. It explains how the sign of b^2 - 4ac determines the number of real roots, which is different from solving simultaneous equations or reading coordinates from two graphs.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: exam_style.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.