plumiQuadratic graphs and turning points: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on A11 Quadratic graphs and turning points, 2017–2025, with its mark scheme and examiner’s report.
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All 25 questions on Quadratic graphs and turning points, as a list
- June 2025, Paper 1H, Q23 (4 marks): (a) Write x2 + 12x + 50 in the form (x + a)2 + b where a and b are integers. Answer 23 (b) A curve has the equation y = (x – 3)2 – 8 Write down the coordinates
- June 2025, Paper 3H, Q23 (2 marks): A roller coaster starts at ground level. The height above ground level, h, in metres, of the roller coaster is given by h = – (t – 7)2 + 49 where t is the time
- November 2024, Paper 1H, Q18 (4 marks): (a) Express x2 + 8x – 5 in the form (x + a)2 – b where a and b are integers. Answer 18 (b) A curve has the equation y = (x – 7)2 + 8 Write down the coordinates
- November 2024, Paper 2H, Q22 (3 marks): The nth term of a sequence is n2 – 30n + 236 By completing the square, show that all the terms of the sequence have two or more digits.
- June 2024, Paper 2H, Q5 (4 marks): (a) Here is a sketch of the graph y = –2x + 6 Complete the coordinates of C and D. C ( 0 , ) D ( , 0 ) 5 (b) Here is a sketch of a quadratic graph. Complete the
- June 2024, Paper 3H, Q13 (2 marks): Here is a quadratic graph with equation y = f(x) Write down the roots of the equation f(x) = 0 Answer
- November 2023, Paper 2H, Q18 (3 marks): By completing the square, prove that x2 + 6x + 13 is always positive.
- November 2023, Paper 3H, Q17 (1 mark): Here is a sketch of the quadratic graph y = f(x) The graph crosses the x-axis at x = a and x = b Write an expression for the x-coordinate of the turning point.
- November 2022, Paper 1H, Q16 (4 marks): A graph has the equation y = x2 + px + r where p and r are constants. The graph passes through the points (0, 4), (1, 3) and (8, w) Work out the value of w. w =
- June 2022, Paper 2H, Q29 (3 marks): The equation of a curve is y = x2 – 18x + 70 By completing the square, work out the coordinates of the turning point. You must show your working. Answer ( , )
- June 2022, Paper 3H, Q6 (3 marks): Here is a sketch of the curve y = x2 – 4x – 5 6 (a) Write down the two roots of x2 – 4x – 5 = 0 Answer and 6 (b) Work out the coordinates of T, the turning poin
- November 2021, Paper 2H, Q25 (3 marks): The equation of a curve is y = x2 + 14x + 52 By completing the square, work out the coordinates of the turning point. You must show your working. Answer ( , )
- November 2020, Paper 2H, Q7 (3 marks): Here is the graph of y = x2 – 7x + 10 for values of x from 0 to 7 7 (a) Write down the roots of x2 – 7x + 10 = 0 Answer 7 (b) Write down the x-coordinate of the
- November 2020, Paper 3H, Q27 (1 mark): The equation of a curve is y = (x – 1)2 – 6 Circle the coordinates of the turning point. (–1, –6) (1, 6) (–1, 6) (1, –6)
- November 2019, Paper 1H, Q27 (4 marks): A curve has the equation y = x2 – 6x + 17 The turning point of the curve is at (a, 8) 27 (a) By completing the square, or otherwise, work out the value of a. An
- June 2019, Paper 1H, Q26 (3 marks): The turning point of the graph y = (x + a)2 + b has x-coordinate –2 (3, 1) is another point on the graph. Work out the y-coordinate of the turning point. Answer
- November 2018, Paper 1H, Q25 (3 marks): A quadratic curve intersects the axes at (–3, 0), (3, 0) and (0, 18) Work out the equation of the curve. Not drawn accurately Answer
- November 2018, Paper 3H, Q28 (1 mark): Here is a sketch of a quadratic curve. The turning point is (3, –2) Not drawn accurately Circle the correct statement about the gradient of the curve for x < 3
- June 2018, Paper 1H, Q29 (4 marks): Here are sketches of two graphs. The graph of y = x2 – 1 is translated 3 units to the left to give graph A. 29 (a) The equation of graph A can be written in the
- November 2017, Paper 1H, Q23 (1 mark): The equation of a curve is y = (x + 3)2 + 5 Circle the coordinates of the turning point. (5, 3) (5, –3) (3, 5) (–3, 5)
- November 2017, Paper 3H, Q29 (2 marks): Here is the graph of y = f(x) where f(x) is a quadratic function. Write down all the integer solutions of f(x) ⩾ 0 Answer
- June 2017, Paper 2H, Q6 (5 marks): (a) Complete the table of values for y = x2 − x − 2 x −2 −1 0 1 2 3 y −2 −2 4 6 (b) Draw the graph of y = x2 − x − 2 for values of x from −2 to 3 6 (c) Write do
- June 2017, Paper 3H, Q21 (1 mark): Here is a sketch of y = f(x) where f(x) is a quadratic function. The graph intersects the x-axis where x = –2.5 and x = 1 Not drawn accurately Circle the soluti
- June 2017, Paper 3H, Q23 (4 marks): Here is a sketch of y = x2 + bx + c The curve intersects the x-axis at (5, 0) and point P the y-axis at (0, –10) Work out the x-coordinate of the turning point
- Specimen, Paper 2H, Q25 (6 marks): 2x2 6x + 5 can be written in the form a(x b)2 + c where a, b and c are positive numbers. 25 (a) Work out the values of a, b and c. a = b = c = 25 (b) Using
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