2.3.1 Quadratic functions, graphs and the discriminant Quiz: Pearson Edexcel Maths, Unit 2

The 20 questions

1. What is the shape of the graph of any quadratic function y = ax² + bx + c?

   • Parabola
   • Hyperbola
   • Ellipse
   • Cubic curve

2. What condition on coefficient a applies for a quadratic graph to have a minimum point?

   • a ≠ 0
   • a > 0
   • a = 0
   • a < 0

3. What condition on coefficient a applies for a quadratic graph to have a maximum point?

   • a > 0
   • a < 0
   • a = 0
   • a = 1

4. What formula defines the discriminant used to determine the nature of quadratic roots?

   • b² - 4ac
   • b² + 4ac
   • 4ac - b²
   • b + 4ac

5. What does a positive discriminant indicate about the roots of a quadratic?

   • Two distinct real roots
   • No real roots
   • Complex conjugate roots
   • One repeated root

6. What does a discriminant equal to zero indicate about the roots?

   • No real roots
   • Undefined roots
   • Two distinct real roots
   • One repeated root

7. What does a negative discriminant indicate about the roots of a quadratic?

   • Two distinct real roots
   • No real roots
   • One repeated root
   • Infinite roots

8. What algebraic method rewrites ax² + bx + c in the form a(x + p)² + q?

   • Integration by parts
   • Factorisation
   • Completing the square
   • Polynomial division

9. Find the discriminant of the quadratic expression x² + 4x + 4.

   • 4
   • -16
   • 0
   • 16

10. Find the discriminant of the quadratic expression 2x² - 3x + 1.

    • 1
    • 17
    • -1
    • 7

11. What is the y-intercept of the quadratic graph y = 3x² - 5x + 7?

    • 3
    • 7
    • 0
    • -5

12. What is the x-coordinate of the turning point of y = (x - 3)² + 5?

    • 5
    • 3
    • -3
    • -5

13. What is the y-coordinate of the minimum point of y = (x - 3)² + 5?

    • -5
    • -3
    • 5
    • 3

14. For which range of k does the quadratic x² + kx + 4 = 0 have distinct real roots?

    • k = 4
    • k < -4 or k > 4
    • k > 4
    • -4 < k < 4

15. What is the line of symmetry for the parabola y = x² - 6x + 5?

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

16. Find the maximum value of the quadratic expression 5 - 2x - x².

    • 1
    • 6
    • 5
    • -1

17. What does a quadratic graph touching the x-axis at a single point imply?

    • Coefficient a is zero
    • Discriminant is negative
    • Discriminant equals zero
    • Discriminant is positive

18. What is the exact range of values for k if kx² + 4x + 1 = 0 has real roots?

    • k > 4
    • k >= 4
    • k < 4
    • k <= 4

19. What are the roots of the quadratic equation x² - 9 = 0?

    • 0 and 3
    • 3 and -3
    • 3 only
    • 9 and -9

20. How many real roots does the quadratic equation x² + 2x + 5 = 0 possess?

    • One
    • Infinite
    • Zero
    • Two

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