10 questions · Form 4 Mathematics Bab 1: Quadratic Functions and Equations in One Variable
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.
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.
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?
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.
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.
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?
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?
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?
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?
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.
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.
Answer: A
Axis of symmetry x = --b2 × 1 = b2. Setting b2 = 4 yields b = 8.