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Quiz Chapter 2: Quadratic Functions

10 questions · Form 4 Additional Mathematics Bab 1: Quadratic Functions

Question 1 of 10Score: 0

Find the minimum value of the quadratic function f(x) = 2(x + 1)² - 9.

Full Question List & Answer Key

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

1. Find the minimum value of the quadratic function f(x) = 2(x + 1)² - 9.

  1. -1
  2. -9
  3. 2
  4. 9
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Answer: B

In vertex form f(x) = a(x - h)² + k with a = 2 > 0, the minimum value is given directly by k, which is -9.

2. If α and β are roots of 2x² - 6x + 3 = 0, find the value of α + β.

  1. -3
  2. 3
  3. 32
  4. -32
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Answer: B

Sum of roots α + β = -ba = --62 = 62 = 3.

3. If α and β are the roots of x² - 5x + 2 = 0, evaluate α² + β².

  1. 21
  2. 25
  3. 29
  4. 23
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Answer: A

SOR α + β = 5, POR αβ = 2. Use identity: α² + β² = (α + β)² - 2αβ = (5)² - 2(2) = 25 - 4 = 21.

4. 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.

5. 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.

6. What is the condition for a quadratic equation ax² + bx + c = 0 to have two real and equal roots?

  1. b² - 4ac > 0
  2. b² - 4ac < 0
  3. b² - 4ac = 0
  4. b² - 4ac ≥ 0
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Answer: C

A quadratic equation has two equal real roots (one repeated root) if and only if its discriminant b² - 4ac = 0.

7. Find the quadratic equation whose roots are reciprocal to the roots of 3x² - 7x + 2 = 0.

  1. 2x² - 7x + 3 = 0
  2. 3x² + 7x + 2 = 0
  3. 2x² + 7x + 3 = 0
  4. 7x² - 3x + 2 = 0
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Answer: A

Roots of original equation: SOR = 73, POR = 23. For reciprocal roots 1/α and 1/β: New SOR = (α+β)/(αβ) = (73)/(23) = 72. New POR = 1/(αβ) = 32. Equation: x² - (72)x + 32 = 0 => 2x² - 7x + 3 = 0.

8. 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).

9. What is the axis of symmetry for the quadratic function f(x) = 2x² - 8x + 5?

  1. x = -2
  2. x = 4
  3. x = 2
  4. x = 8
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Answer: C

Axis of symmetry formula: x = -b2a = --82 * 2 = 84 = 2.

10. The quadratic graph f(x) = ax² + bx + c has a maximum point. Which condition MUST be true for a?

  1. a > 0
  2. a = 0
  3. a < 0
  4. a ≥ 1
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Answer: C

A quadratic function has a maximum turning point (∩-shape) if and only if the coefficient of x² is negative, i.e., a < 0.

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