Interpreting Quadratic Graphs · CSEC Mathematics

42 past-paper questions on Interpreting Quadratic Graphs, part of RELATIONS, FUNCTIONS AND GRAPHS, from every CSEC Mathematics paper on Quelpr.

1. 8(b)(ii)1 mark· CSEC Mathematics · 2021 · Paper 2Write down the maximum or minimum value of the function.
2. Q501 mark · multiple choice· CSEC Mathematics · January 2013 · Paper 1The maximum point of y = 4x - x^2 is
3. Q511 mark · multiple choice· CSEC Mathematics · January 2013 · Paper 1The values of x at the points where y = 4x - x^2 intersects y = 0 are
4. Q461 mark · multiple choice· CSEC Mathematics · May/June 2012 · Paper 1The maximum point of y = 4x - x^2 is
5. Q501 mark · multiple choice· CSEC Mathematics · May/June 2015 · Paper 1Items 49-50 refer to the graph below. The values of x at the points where y = 4x - x^2 intersects y = 0 are
6. 4(d)(i)1 mark· Mathematics Q4 4(d)(i)The values of x for which x²-2x-3 = 0 are ____________ and ____________
7. 4(d)(ii)1 mark· Mathematics Q4 4(d)(ii)The minimum value of x² - 2x - 3 is ____________
8. 5(b)2 marks· Mathematics Q5 5(b)values of x for which x²-2x-3= 0
9. 5(b)(ii)2 marks· Mathematics Q5 5(b)(ii)Use the graph above to determine the value of y for which x = -1.5
10. 5(b)(iii)2 marks· Mathematics Q5 5(b)(iii)Use the graph above to determine the values of x for which y = 0
11. 5(b)(iv)2 marks· Mathematics Q5 5(b)(iv)Use the graph above to determine the range of values of y, giving your answer in the form a ≤ y ≤ b, where a and b are real numbers.
12. 5(d)2 marks· Mathematics Q5 5(d)whole number values of x for which x²-2x-3<1
13. 5(e)3 marks· Mathematics Q5 5(e)gradient of f(x) = x²-2x-3 at x = 2.
14. 6(b)(iii)3 marks· Mathematics Q6 6(b)(iii)Using information from your graph, complete EACH of the following statements: The minimum value of y = x^2 - 2x – 3 occurs when x = (blank) and The values of x for which x^2 - 2x - 3 = x + 3 are x = (blank) and x =…
15. 6(c)2 marks· Mathematics Q6 6(c)Using your graph, estimate the value of y when x = 3.5. Show on your graph how the value was obtained.
16. 6(d)2 marks· Mathematics Q6 6(d)Estimate the gradient of the tangent to the curve at (2, 4).
17. 6(d)(ii)1 mark· Mathematics Q6 6(d)(ii)Estimate the minimum value of the function y.
18. 6(d)(iii)1 mark· Mathematics Q6 6(d)(iii)State the values of the solutions of the equation: x² – 2x – 3 = 0.
19. 7(c)(ii)2 marks· Mathematics Q7 7(c)(ii)State the x-coordinates of the two points at which the curve meets the line.
20. 7(i)1 mark· Mathematics Q7 7(i)Using the graph above, determine the value of f(x) when x = 0.
21. 7(ii)2 marks· Mathematics Q7 7(ii)Using the graph above, determine the values of x when f(x) = 0.
22. 7(iii)2 marks· Mathematics Q7 7(iii)Using the graph above, determine the coordinates of the maximum point.
23. 7(iv)2 marks· Mathematics Q7 7(iv)Using the graph above, determine the equation of the axis of symmetry.
24. 7(v)2 marks· Mathematics Q7 7(v)Using the graph above, determine the values of x when f(x) = 5.
25. 7(vi)2 marks· Mathematics Q7 7(vi)Using the graph above, determine the interval within which x lies when f(x) > 5. Write your answer in the form a < x < b.
26. 8(a)(iii)a)1 mark· Mathematics Q8 8(a)(iii)a)Using the graph on page 26, determine the coordinates of the maximum point of f(x).
27. 8(a)(iii)b)2 marks· Mathematics Q8 8(a)(iii)b)Using the graph on page 26, determine the range of values of x for which f(x) > 0.
28. 8(a)(iii)c)1 mark· Mathematics Q8 8(a)(iii)c)Using the graph on page 26, determine the gradient of f(x) at x = 1.
29. 8(c)(i)1 mark· Mathematics Q8 8(c)(i)Using your graph, calculate estimates of the GREATEST height above the ground reached by the ball.
30. 8(c)(ii)2 marks· Mathematics Q8 8(c)(ii)Using your graph, calculate estimates of the number of seconds for which the ball was MORE than 12 metres above the ground.
31. 8(c)(iii)1 mark· Mathematics Q8 8(c)(iii)Using your graph, calculate estimates of the interval of time during which the ball was moving upwards.
32. 9(a)(ii)2 marks· Mathematics Q9 9(a)(ii)State, giving the reason for your answer, whether the line y = 8 - x is a tangent to the curve 2x² + xy = -16.
33. 9(b)(i)2 marks· Mathematics Q9 9(b)(i)Use the graph to solve the equation x² - 6x + 8 = 0.
34. 9(b)(i)2 marks· Mathematics Q9 9(b)(i)State the roots of the equation x² + bx + c = 0.
35. 9(b)(ii)a)2 marks· Mathematics Q9 9(b)(ii)a)Determine the value of c.
36. 9(b)(ii)b)2 marks· Mathematics Q9 9(b)(ii)b)Show that b = -4.
37. 9(b)(iii)b)3 marks· Mathematics Q9 9(b)(iii)b)Copy the sketch and state the x-coordinate of C.
38. 9(c)(ii)4 marks· Mathematics Q9 9(c)(ii)On your graph, draw a tangent to the curve at the point where x = 2. Extend the tangent to intersect the x and y axes. Using your tangent, estimate the gradient of f(x) at x = 2.
39. 9(c)(ii)b)3 marks· Mathematics Q9 9(c)(ii)b)Use your graph to estimate the rate of cooling of the liquid at t = 30 minutes.
40. 10(d)4 marks· Mathematics Q10 10(d)Draw the tangent to the curve at the point (3, 2.2) as accurately as possible. Hence, estimate the gradient of the curve at the point (3, 2.2). [Show clearly on your graph how the estimates at (c) (i), (ii) and (d) were…
41. 11(a)(iii)1 mark· Mathematics Q11 11(a)(iii)Use your graph to estimate the value of x when y = 0.7.
42. 12(b)(iii)7 marks· Mathematics Q12 12(b)(iii)Using the graph, or otherwise, determine the value of x for which 2 - cos x = 1.8.