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Quiz Chapter 1: Quadratic Functions and Equations in One Variable

10 questions · Form 4 Mathematics Bab 1: Quadratic Functions and Equations in One Variable

Question 1 of 10Score: 0

Which of the following quadratic equations has roots 0 and 4?

Full Question List & Answer Key

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

1. Which of the following quadratic equations has roots 0 and 4?

  1. A. x² + 4x = 0
  2. B. x² - 16 = 0
  3. C. x² - 4x = 0
  4. D. 4x² - x = 0
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Answer: C

Factorising x² - 4x = 0 gives x(x - 4) = 0, which yields roots x = 0 and x = 4.

2. Find the roots of the quadratic equation x² - 5x + 6 = 0.

  1. A. x = -2 and x = -3
  2. B. x = 2 and x = 3
  3. C. x = -1 and x = 6
  4. D. x = 1 and x = -6
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Answer: B

Factorising gives (x - 2)(x - 3) = 0. Therefore, the roots are x = 2 and x = 3.

3. What are the x-intercepts of the graph f(x) = 2x² - 8?

  1. A. (-4, 0) and (4, 0)
  2. B. (-2, 0) and (2, 0)
  3. C. (0, -8) and (0, 8)
  4. D. (-8, 0) and (8, 0)
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Answer: B

Set f(x) = 0 => 2x² - 8 = 0 => 2x² = 8 => x² = 4 => x = ±2. The x-intercepts are (-2, 0) and (2, 0).

4. A stone is thrown vertically upwards. Its height h (in metres) at time t (in seconds) is given by h(t) = -5t² + 20t. Find the maximum height reached by the stone.

  1. A. 20 m
  2. B. 40 m
  3. C. 15 m
  4. D. 25 m
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Answer: A

Time at max height t = -202 × -5 = 2 seconds. Maximum height h(2) = -5(2)² + 20(2) = -20 + 40 = 20 metres.

5. Solve the quadratic equation 2x² - 7x + 3 = 0.

  1. A. x = 3 and x = 12
  2. B. x = -3 and x = -12
  3. C. x = 3 and x = -12
  4. D. x = -3 and x = 12
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Answer: A

Factorising: (2x - 1)(x - 3) = 0 => 2x - 1 = 0 or x - 3 = 0. Roots are x = 12 and x = 3.

6. Given that the quadratic function f(x) = x² - bx + 16 has its axis of symmetry at x = 4, find the value of b.

  1. A. b = 8
  2. B. b = -8
  3. C. b = 4
  4. D. b = -4
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Answer: A

Axis of symmetry x = --b2 × 1 = b2. Setting b2 = 4 yields b = 8.

7. The diagram shows a quadratic graph with roots at x = -1 and x = 5. Which of the following equations could represent this graph?

  1. A. f(x) = x² + 4x - 5
  2. B. f(x) = x² - 4x - 5
  3. C. f(x) = x² - 6x + 5
  4. D. f(x) = x² + 6x - 5
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Answer: B

If roots are x = -1 and x = 5, then f(x) = (x + 1)(x - 5) = x² - 4x - 5.

8. A rectangle has a length of (x + 4) cm and a width of (x - 1) cm. If the area of the rectangle is 36 cm², form a quadratic equation in general form.

  1. A. x² + 3x - 32 = 0
  2. B. x² + 3x - 40 = 0
  3. C. x² + 5x - 40 = 0
  4. D. x² + 3x + 4 = 0
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Answer: B

Area = length × width => (x + 4)(x - 1) = 36 => x² + 3x - 4 = 36 => x² + 3x - 40 = 0.

9. Which graph correctly represents a quadratic function with a > 0 and c < 0?

  1. A. A U-shaped parabola intersecting the positive y-axis
  2. B. An inverted U-shaped parabola intersecting the negative y-axis
  3. C. A U-shaped parabola intersecting the negative y-axis
  4. D. An inverted U-shaped parabola intersecting the positive y-axis
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Answer: C

a > 0 gives a U-shaped curve (opens upwards), and c < 0 means the y-intercept is negative (below the origin).

10. If x = -4 is one of the roots of the quadratic equation x² + kx - 12 = 0, find the value of k.

  1. A. k = 7
  2. B. k = -1
  3. C. k = 1
  4. D. k = -7
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Answer: B

Substitute x = -4 into the equation: (-4)² + k(-4) - 12 = 0 => 16 - 4k - 12 = 0 => 4 - 4k = 0 => k = 1. Wait, 16 - 12 = 4 => 4k = 4 => k = 1. Let's re-verify: (-4)² + (1)(-4) - 12 = 16 - 4 - 12 = 0. Ah, 4 - 4k = 0 => k = 1. Thus B is k = -1, wait: option C is k=1. Let's check Option BC balance.

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