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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. Convert the equation (2x - 3)² = 25 into general quadratic form ax² + bx + c = 0.

  1. A. 4x² - 12x - 16 = 0
  2. B. 4x² - 12x + 34 = 0
  3. C. 4x² - 6x - 16 = 0
  4. D. 4x² - 12x - 34 = 0
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Answer: A

Expand: 4x² - 12x + 9 = 25 => 4x² - 12x + 9 - 25 = 0 => 4x² - 12x - 16 = 0.

2. 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.

3. 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.

4. 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).

5. 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.

6. Determine the coordinates of the minimum point of the function f(x) = x² - 6x + 5.

  1. A. (-3, 32)
  2. B. (3, -4)
  3. C. (3, 4)
  4. D. (-3, -4)
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Answer: B

x = -b2a = --62 × 1 = 3. Substituting x = 3: f(3) = (3)² - 6(3) + 5 = 9 - 18 + 5 = -4. Minimum point is (3, -4).

7. 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.

8. Which statement is TRUE regarding the graph of f(x) = -x² + 4x + 12?

  1. A. It has a minimum value of 16.
  2. B. Its y-intercept is at (0, -12).
  3. C. Its axis of symmetry is x = 2.
  4. D. It does not intersect the x-axis.
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Answer: C

Axis of symmetry x = -42 × -1 = 2. Maximum value = -(2)² + 4(2) + 12 = 16, and y-intercept is (0, 12).

9. How does the value of 'a' affect the graph of f(x) = ax² + bx + c?

  1. A. It determines the y-intercept of the graph.
  2. B. It determines the horizontal shift of the axis of symmetry.
  3. C. It determines the shape and width of the opening of the curve.
  4. D. It determines the number of x-intercepts only.
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Answer: C

The sign of 'a' controls direction (up/down) and the magnitude of 'a' controls the width of the parabola.

10. What is the y-intercept of the quadratic function f(x) = 3x² - 5x - 8?

  1. A. (0, -8)
  2. B. (0, 3)
  3. C. (0, -5)
  4. D. (-8, 0)
Show answer

Answer: A

The y-intercept occurs when x = 0. Substituting x = 0 gives f(0) = -8. Thus, the point is (0, -8).

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