Sketching quadratic graphs
AQA GCSE Maths revision on Sketching quadratic graphs. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 18 practice questions on this topic.
Sample questions (3 of 18)
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Question 1
A student sketches y = x squared + 5 and y = x squared - 5. How does the position of the second graph compare to the first?
- A) It is translated 10 units down
- B) It is translated 5 units left
- C) It is translated 5 units down
- D) It is reflected in the x-axis
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Answer: It is translated 5 units down
In quadratic functions of the form y = f(x) + c, the constant 'c' represents a vertical shift. Since the constant changed from +5 to -5, the entire parabola moves downwards by 10 units in total, but relative to the origin, the vertex shift is specifically 5 units down from the original position.
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Question 2
Which feature of the quadratic equation y = ax squared + bx + c determines whether the parabola has a 'u' shape or an 'n' shape?
- A) The value of c
- B) The sign of a
- C) The value of b
- D) The discriminant
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Answer: The sign of a
Hint: The coefficient of the squared term dictates the concavity of the graph.
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Question 3
A student sketches y = (x - 3) squared. Why is the vertex NOT at (3, 0)?
- A) The vertex is actually at (-3, 0)
- B) The vertex is at (3, 0), the student is mistaken
- C) The vertex is at (0, 3)
- D) The vertex is at (0, -3)
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Answer: The vertex is at (3, 0), the student is mistaken
When a quadratic is written in the form y = (x - h) squared + k, the vertex is located at (h, k). In this specific case, h is 3 and k is 0, so the vertex must be at (3, 0).
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