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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

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Full Question List & Answer Key

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

1. For the quadratic function f(x) = -2x² + 8x - 5, what type of turning point does the graph have?

  1. A. Minimum point because a > 0
  2. B. Maximum point because a < 0
  3. C. Minimum point because a < 0
  4. D. Maximum point because a > 0
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Answer: B

Since the coefficient of x² is negative (a = -2 < 0), the parabola opens downwards and has a maximum turning point.

2. 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.

3. Which of the following is a quadratic expression in one variable?

  1. A. 3x² + 2y - 5
  2. B. 4x³ - x² + 2
  3. C. 5x² - 3x + 7
  4. D. 2x² + 3x - 1
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Answer: C

A quadratic expression in one variable has a single variable with a highest exponent power of 2. Option C satisfies this condition.

4. Determine the equation of the axis of symmetry for the function f(x) = 2x² - 12x + 9.

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

The formula for axis of symmetry is x = -b2a. Here, a = 2, b = -12. So x = --122 × 2 = 124 = 3.

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. 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.

7. 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).

8. 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.

9. 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.

10. Given f(x) = ax² + bx + c, if b = 0, what can be concluded about the graph?

  1. A. The graph passes through the origin.
  2. B. The axis of symmetry is the x-axis.
  3. C. The axis of symmetry is the y-axis (x = 0).
  4. D. The graph has no real roots.
Show answer

Answer: C

When b = 0, the axis of symmetry equation x = -b2a becomes x = 0, which is the y-axis.

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