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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. 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
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Answer: D

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

2. 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
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Answer: B

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

3. If the quadratic equation x² - px + 9 = 0 has equal roots, find the possible values of p.

  1. p = 6 only
  2. p = -6 only
  3. p = ± 6
  4. p = ± 3
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Answer: C

Equal roots => b² - 4ac = 0 => (-p)² - 4(1)(9) = 0 => p² - 36 = 0 => p² = 36 => p = ±6.

4. The quadratic function f(x) = (x - p)² + q has a vertex at (-4, -3). What are the values of p and q?

  1. p = 4, q = -3
  2. p = -4, q = -3
  3. p = -4, q = 3
  4. p = 4, q = 3
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Answer: B

Compare f(x) = (x - p)² + q with vertex (h, k) = (-4, -3): h = p = -4, k = q = -3.

5. Solve the inequality (x - 2)(x - 6) ≥ 0.

  1. x ≤ 2 or x ≥ 6
  2. 2 ≤ x ≤ 6
  3. x ≤ -6 or x ≥ -2
  4. x ≤ 6
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Answer: A

Critical values are x = 2 and x = 6. For '≥ 0' with a positive leading coefficient, solution is outside the roots: x ≤ 2 or x ≥ 6.

6. Find the range of values of k for which the equation x² + 4x + k = 0 has two distinct real roots.

  1. k < 4
  2. k > 4
  3. k ≤ 4
  4. k = 4
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Answer: A

Two distinct roots require b² - 4ac > 0 => (4)² - 4(1)(k) > 0 => 16 - 4k > 0 => 4k < 16 => k < 4.

7. 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
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Answer: A

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

8. 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
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Answer: A

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

9. 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)
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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).

10. Find the roots of the quadratic equation 2x² - 5x - 3 = 0.

  1. x = 3 or x = -12
  2. x = -3 or x = 12
  3. x = 3 or x = 12
  4. x = -3 or x = -12
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Answer: A

Factorising gives (2x + 1)(x - 3) = 0 => 2x + 1 = 0 or x - 3 = 0 => x = -12 or x = 3.

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