arrow_backBack to Study Resources

Quiz Chapter 2: Quadratic Functions

10 questions · Form 4 Additional Mathematics Bab 1: Quadratic Functions

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Find the range of values of x for which f(x) = 2x² - 8x is negative.

  1. 0 < x < 4
  2. x < 0 or x > 4
  3. -4 < x < 0
  4. x < -4 or x > 0
Show answer

Answer: A

Negative means f(x) < 0 => 2x(x - 4) < 0. Critical values are x = 0 and x = 4. Solution: 0 < x < 4.

2. If α and β are roots of 2x² - 6x + 3 = 0, find the value of α + β.

  1. -3
  2. 3
  3. 32
  4. -32
Show answer

Answer: B

Sum of roots α + β = -ba = --62 = 62 = 3.

3. The graph of f(x) = ax² + bx + c does NOT intersect the x-axis. Which statement must be TRUE?

  1. b² - 4ac > 0
  2. b² - 4ac = 0
  3. b² - 4ac ≥ 0
  4. b² - 4ac < 0
Show answer

Answer: D

No intersection with the x-axis means the quadratic equation f(x) = 0 has no real roots, so b² - 4ac < 0.

4. What is the condition for a quadratic equation ax² + bx + c = 0 to have two real and equal roots?

  1. b² - 4ac > 0
  2. b² - 4ac < 0
  3. b² - 4ac = 0
  4. b² - 4ac ≥ 0
Show answer

Answer: C

A quadratic equation has two equal real roots (one repeated root) if and only if its discriminant b² - 4ac = 0.

5. The quadratic function f(x) = -(x - 3)² + 7 has a turning point at (h, k). State the coordinates and nature of the turning point.

  1. Minimum point at (3, 7)
  2. Maximum point at (-3, 7)
  3. Maximum point at (3, 7)
  4. Minimum point at (-3, 7)
Show answer

Answer: C

Since a = -1 < 0, the graph is maximum shaped (∩). From f(x) = a(x - h)² + k, vertex is (h, k) = (3, 7).

6. State the y-intercept of the quadratic graph f(x) = -2(x - 1)² + 8.

  1. (0, 8)
  2. (0, 6)
  3. (0, -2)
  4. (0, 10)
Show answer

Answer: B

y-intercept occurs when x = 0: f(0) = -2(0 - 1)² + 8 = -2(1) + 8 = 6. Thus, y-intercept is (0, 6).

7. Express f(x) = x² - 6x + 13 in vertex form by completing the square.

  1. (x - 3)² + 22
  2. (x - 3)² + 4
  3. (x + 3)² + 4
  4. (x - 6)² + 13
Show answer

Answer: B

f(x) = x² - 6x + (-3)² - (-3)² + 13 = (x - 3)² - 9 + 13 = (x - 3)² + 4.

8. If α and β are the roots of x² - 5x + 2 = 0, evaluate α² + β².

  1. 21
  2. 25
  3. 29
  4. 23
Show answer

Answer: A

SOR α + β = 5, POR αβ = 2. Use identity: α² + β² = (α + β)² - 2αβ = (5)² - 2(2) = 25 - 4 = 21.

9. Given the quadratic curve f(x) = 3x² + bx + 12 touches the x-axis at a single point, find the positive value of b.

  1. 12
  2. 6
  3. 144
  4. 24
Show answer

Answer: A

Touches x-axis => b² - 4ac = 0 => b² - 4(3)(12) = 0 => b² - 144 = 0 => b² = 144 => b = 12 (positive value).

10. Form a quadratic equation with roots -2 and 5.

  1. x² - 3x - 10 = 0
  2. x² + 3x - 10 = 0
  3. x² - 7x + 10 = 0
  4. x² + 3x + 10 = 0
Show answer

Answer: A

SOR = -2 + 5 = 3. POR = (-2)(5) = -10. Equation: x² - (SOR)x + (POR) = 0 => x² - 3x - 10 = 0.

Sponsored