10 questions · Form 4 Additional Mathematics Bab 1: Quadratic Functions
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Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Form a quadratic equation with roots -2 and 5.
Answer: A
SOR = -2 + 5 = 3. POR = (-2)(5) = -10. Equation: x² - (SOR)x + (POR) = 0 => x² - 3x - 10 = 0.
2. Given the quadratic curve f(x) = 3x² + bx + 12 touches the x-axis at a single point, find the positive value of b.
Answer: A
Touches x-axis => b² - 4ac = 0 => b² - 4(3)(12) = 0 => b² - 144 = 0 => b² = 144 => b = 12 (positive value).
3. Find the quadratic equation whose roots are reciprocal to the roots of 3x² - 7x + 2 = 0.
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.
4. Find the range of values of x for which f(x) = 2x² - 8x is negative.
Answer: A
Negative means f(x) < 0 => 2x(x - 4) < 0. Critical values are x = 0 and x = 4. Solution: 0 < x < 4.
5. Find the range of values of k for which the equation x² + 4x + k = 0 has two distinct real roots.
Answer: A
Two distinct roots require b² - 4ac > 0 => (4)² - 4(1)(k) > 0 => 16 - 4k > 0 => 4k < 16 => k < 4.
6. State the y-intercept of the quadratic graph f(x) = -2(x - 1)² + 8.
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).
7. The graph of f(x) = ax² + bx + c does NOT intersect the x-axis. Which statement must be TRUE?
Answer: D
No intersection with the x-axis means the quadratic equation f(x) = 0 has no real roots, so b² - 4ac < 0.
8. Find the minimum value of the quadratic function f(x) = 2(x + 1)² - 9.
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.
9. What is the axis of symmetry for the quadratic function f(x) = 2x² - 8x + 5?
Answer: C
Axis of symmetry formula: x = -b2a = --82 * 2 = 84 = 2.
10. Solve the inequality (x - 2)(x - 6) ≥ 0.
Answer: A
Critical values are x = 2 and x = 6. For '≥ 0' with a positive leading coefficient, solution is outside the roots: x ≤ 2 or x ≥ 6.