Lesson B3

B3 Quadratic functions, discriminant and completing the square Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson B3, Quadratic functions, discriminant and completing the square: 20 multiple choice questions for the AQA Maths (7357), Unit 2: Algebra and functions, written with Revision Ninja.

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The 20 questions

  1. What is the discriminant of 2x^2 - 4x + 5?

    • 56
    • 24
    • -24
    • -56

  2. For a quadratic ax^2 + bx + c, which condition gives repeated real roots?

    • b^2 - 4ac > 0
    • b^2 - 4ac < 0
    • b^2 - 4ac = 0
    • b^2 + 4ac = 0

  3. When does ax^2 + bx + c = 0 have two distinct real roots?

    • When b^2 - 4ac > 0
    • When b^2 + 4ac > 0
    • When b^2 - 4ac < 0
    • When b^2 - 4ac = 0

  4. Which is x^2 + 6x + 5 written by completing the square?

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

  5. What is the minimum value of x^2 + 6x + 5, and where does it occur?

    • 5 at x = -3
    • 4 at x = -3
    • -4 at x = 3
    • -4 at x = -3

  6. Find the values of k for which x^2 + kx + 9 = 0 has repeated roots.

    • k = 9 only
    • k = 3 only
    • k = 6 or k = -6
    • k = 6 only

  7. For which k does 2x^2 + 3x + k = 0 have no real roots?

    • k > 9/8
    • k > 8/9
    • k >= 9/8
    • k < 9/8

  8. Solve 2x^2 - 5x - 3 = 0.

    • x = -1/2 or x = 3
    • x = 1/2 or x = 3
    • x = 1/2 or x = -3
    • x = -1 or x = 3/2

  9. Solve (x - 1)^2 - 5(x - 1) + 6 = 0.

    • x = 3 or x = 4
    • x = -1 or x = 0
    • x = 2 or x = 3
    • x = 1 or x = 6

  10. What is the vertex of y = -2(x - 1)^2 + 8, and what type of point is it?

    • (1, -8), a minimum
    • (-1, 8), a maximum
    • (1, 8), a maximum
    • (1, 8), a minimum

  11. For which k does y = x^2 - 4x + k touch the x-axis?

    • k = 2
    • k = 4
    • k = -4
    • k = 16

  12. How many real roots does x^2 + 2x + 5 = 0 have?

    • Two distinct real roots
    • Exactly three roots
    • One repeated root
    • None

  13. A rectangle has perimeter 20. What is its maximum possible area?

    • 50
    • 100
    • 25
    • 20

  14. A ball's height in metres is h = 1 + 20t - 5t^2. What is its maximum height and when does it occur?

    • 25 m at t = 2 s
    • 20 m at t = 2 s
    • 21 m at t = 2 s
    • 21 m at t = 4 s

  15. For which c is x^2 + 4x + c > 0 for all real x?

    • c > 16
    • c < 4
    • c >= 4
    • c > 4

  16. For which k does the line y = kx + 1 touch the curve y = x^2 + 3 at exactly one point?

    • k = 4 or k = -4
    • k = sqrt(2) or k = -sqrt(2)
    • k = 2 sqrt(2) or k = -2 sqrt(2)
    • k = 8 or k = -8

  17. Which statement about the turning point of y = ax^2 + bx + c, with a > 0, is correct?

    • It is a minimum point
    • It is always at the origin
    • It always lies on the y-axis
    • It is a maximum point

  18. What is the completed-square form of ax^2 + bx + c?

    • a(x - b/(2a))^2 - c
    • (x + b/(2a))^2 + c - b^2/(4a)
    • a(x + b/(2a))^2 + c - b^2/(4a)
    • a(x + b/a)^2 + c

  19. If a > 0 and the discriminant of ax^2 + bx + c is positive, where does the graph lie relative to the x-axis between the roots?

    • Above the x-axis
    • On the x-axis
    • Below the x-axis
    • Above the x-axis only at the vertex

  20. What are the solutions of (x - 2)^2 = 9?

    • x = 3 or x = -3
    • x = 11 or x = -7
    • x = 5 only
    • x = 5 or x = -1

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