Worksheet Chapter 2: Quadratic Functions

1. True or False: The quadratic equation x² + 2x + 5 = 0 has no real roots.

2. True or False: If the coefficient of x² in a quadratic function is negative (a < 0), the graph has a minimum turning point.

3. Express f(x) = -2x² + 8x - 5 in vertex form f(x) = a(x - h)² + k. Hence, state the maximum turning point and maximum value of the function.

4. Find the range of values of p such that the line y = 2x + p does not intersect the quadratic curve y = x² - 4x + 5.

5. A rectangle has a perimeter of 40 cm. (a) Express the area A of the rectangle in terms of its width x. (b) By completing the square or using vertex properties, calculate the maximum possible area of the rectangle and the corresponding dimensions.

6. One of the roots of the quadratic equation x² + px - 12 = 0 is 3. Find the value of p and the second root.

7. Given that α and β are the roots of the quadratic equation 2x² - 4x - 1 = 0, form a new quadratic equation whose roots are 2α + 1 and 2β + 1.

8. Solve the quadratic inequality 2x² + 5x - 3 ≥ 0.

9. Solve the quadratic equation 3x² - 5x - 2 = 0 by factorisation.

10. Fill in the blank: The value of the discriminant b² - 4ac for a quadratic curve that touches the x-axis at exactly one point is __________.