10 questions · Form 4 Mathematics Bab 1: Quadratic Functions and Equations in One Variable
Which of the following quadratic equations has roots 0 and 4?
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?
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.
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?
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.
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.
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.
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?
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.
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?
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.
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.