Quadratic Equations Quiz

1. What is the standard form of a quadratic equation?

1. ax + b = 0
2. ax² + bx + c = 0
3. x² = c
4. y = mx + c

2. Solve by factorising: x² + 5x + 6 = 0

1. x = −1 or x = −6
2. x = −2 or x = −3
3. x = 1 or x = 6
4. x = 2 or x = 3

3. Solve: x² − 7x + 12 = 0

1. x = −3 or x = −4
2. x = 1 or x = 12
3. x = 3 or x = 4
4. x = 6 or x = 2

4. What is the quadratic formula?

1. x = (−b ± √(b² + 4ac)) / 2a
2. x = (−b ± √(b² − 4ac)) / 2a
3. x = (b ± √(b² + 4ac)) / a
4. x = (b ± √(b² − 4ac)) / 2a

5. Use the quadratic formula to solve: x² + 4x − 5 = 0

1. x = −1 or x = 5
2. x = 1 or x = −5
3. x = 2 or x = −5
4. x = 5 or x = −1

6. What is the discriminant of ax² + bx + c = 0, and what does it tell you?

1. √(b² − 4ac); the number of solutions
2. 2a; whether the parabola opens up or down
3. b² + 4ac; whether the equation has integer solutions
4. b² − 4ac; whether the equation has real solutions

7. How many real solutions does x² + 2x + 5 = 0 have?

1. It depends on x
2. None
3. One
4. Two

8. Solve: x² − 9 = 0

1. x = 3 only
2. x = 3 or x = −3
3. x = 81
4. x = 9

9. Complete the square: write x² + 6x + 2 in the form (x + a)² + b.

1. (x + 3)² + 2
2. (x + 3)² − 11
3. (x + 3)² − 7
4. (x + 6)² − 34

10. Solve: 2x² − 8 = 0

1. x = ±2
2. x = ±4
3. x = 2
4. x = 4

11. Factorise: x² − 25

1. (x + 25)(x − 1)
2. (x + 5)(x − 5)
3. (x − 5)(x − 5)
4. (x − 5)²

12. Solve: x² + x − 6 = 0

1. x = −2 or x = 3
2. x = 2 or x = −3
3. x = 3 or x = 2
4. x = 6 or x = −1

13. A ball is thrown upward. Its height h = −5t² + 20t. When does it hit the ground (h = 0)?

1. t = 0 or t = 4 seconds
2. t = 2 seconds
3. t = 4 seconds
4. t = 5 seconds

14. The parabola y = x² − 4x + 3. What are its x-intercepts?

1. x = −1 and x = −3
2. x = 1 and x = 3
3. x = 2 and x = 1
4. x = 4 and x = 0

15. Solve: 3x² − 12x = 0

1. x = 0 only
2. x = 0 or x = 12
3. x = 0 or x = 4
4. x = 4 only

16. What is the vertex (turning point) of y = (x − 3)² + 5?

1. (−3, 5)
2. (3, −5)
3. (3, 5)
4. (5, 3)

17. Solve using the quadratic formula: 2x² + 3x − 2 = 0

1. x = −0.5 or x = 2
2. x = 0.5 or x = −2
3. x = 1 or x = −2
4. x = 2 or x = 0.5

18. Which of these quadratics has exactly one repeated root?

1. x² + 2x + 5
2. x² + 4x + 3
3. x² − 6x + 9
4. x² − x − 2

19. The sum of a number and its square is 20. Which equation models this?

1. 2x² = 20
2. x + x² = 20
3. x² + x − 20 = 0
4. x² − x − 20 = 0

20. Which direction does the parabola y = −3x² + 2x − 1 open?

1. Downward, because a < 0
2. Left, because b < 0 is absent
3. Right, because c < 0
4. Upward, because a > 0