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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

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.

Full Question List & Answer Key

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

1. 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.

2. 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).

3. 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.

4. Solve the equation 3x(x - 2) = 5 - x and express it in general form.

  1. A. 3x² - 5x - 5 = 0
  2. B. 3x² - 7x - 5 = 0
  3. C. 3x² - 5x + 5 = 0
  4. D. 3x² - 6x - 5 = 0
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Answer: A

Expand: 3x² - 6x = 5 - x => 3x² - 6x + x - 5 = 0 => 3x² - 5x - 5 = 0.

5. 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)
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Answer: A

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

6. 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.

7. 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.

8. 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.

9. 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
Show answer

Answer: A

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

10. 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
Show answer

Answer: A

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

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