A11 Quadratic graphs: roots, intercepts and turning points Quiz: AQA Maths, Unit 2

The 20 questions

1. For y = x^2 - 5x + 6, what are the roots?

   • x = 2 and x = 3
   • x = 1 and x = 6
   • x = -2 and x = -3
   • x = 5 and x = 6

2. What is the y-intercept of y = x^2 - 5x + 6?

   • 5
   • 2
   • 6
   • -5

3. What are the coordinates of the turning point of y = (x - 2)^2 + 1?

   • (1, 2)
   • (2, -1)
   • (2, 1)
   • (-2, 1)

4. For y = -x^2 + 4, is the turning point a maximum or a minimum, and where is it?

   • Minimum, at (0, 4)
   • Maximum, at (4, 0)
   • Maximum, at (0, 4)
   • Minimum, at (0, -4)

5. What is the equation of the line of symmetry of y = x^2 - 6x + 2?

   • x = -3
   • x = -6
   • x = 6
   • x = 3

6. What are the roots of y = (x + 4)(x - 1)?

   • x = 4 and x = -1
   • x = 1 and x = 4
   • x = -4 and x = 1
   • x = -4 and x = -1

7. What are the solutions of x^2 = 9?

   • x = 9 only
   • x = 3 or x = -3
   • x = 81 or x = -81
   • x = 3 only

8. How many times does y = x^2 + 4 cross the x-axis?

   • Four
   • Zero
   • Two
   • One

9. How many times does y = x^2 - 4x + 4 meet the x-axis?

   • Zero
   • Three
   • One
   • Two

10. The height of a rocket is a quadratic function of time with roots at t = 0 and t = 4. What do the roots mean?

    • The height is zero at t = 0 and t = 4 seconds
    • The height is 4 metres at t = 0
    • The height is at its maximum at t = 2 seconds
    • The height is negative at t = 4 seconds

11. What are the coordinates of the turning point of y = x^2 + 6x + 5?

    • (3, 4)
    • (-6, 5)
    • (-3, 4)
    • (-3, -4)

12. (H) Write x^2 + 6x + 5 in completed square form.

    • (x + 3)^2 + 4
    • (x + 6)^2 - 31
    • (x + 3)^2 - 4
    • (x - 3)^2 - 4

13. What is the y-intercept of y = 2x^2 - 3x + 7?

    • -3
    • -7
    • 7
    • 2

14. What are the roots of x^2 - 9x = 0?

    • x = 9 only
    • x = 3 and x = -3
    • x = 0 and x = 9
    • x = -9 and x = 0

15. What are the roots of x^2 - x - 12 = 0?

    • x = 4 and x = -3
    • x = -4 and x = 3
    • x = 12 and x = -1
    • x = 3 and x = 4

16. The height of a ball is h = 20t - 5t^2 metres. After how many seconds is it back at height zero?

    • After 5 seconds
    • After 4 seconds
    • After 20 seconds
    • After 2 seconds

17. For y = 3x^2 - 12x + 1, what is the x-coordinate of the turning point?

    • x = 2
    • x = 12
    • x = 6
    • x = -2

18. A quadratic has roots at x = -1 and x = 5. Where is its turning point?

    • At x = 2
    • At x = -3
    • At x = 6
    • At x = 3

19. (H) What are the coordinates of the minimum turning point of y = 2(x - 1)^2 - 8?

    • (1, -8)
    • (-1, -8)
    • (1, 8)
    • (-1, 8)

20. (H) Which pair gives the roots and y-intercept of y = x^2 - 2x - 8?

    • Roots -8 and 1; y-intercept -2
    • Roots -2 and 4; y-intercept -8
    • Roots 2 and -4; y-intercept 8
    • Roots 2 and 4; y-intercept -8

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