Worksheet Chapter 1: Quadratic Functions and Equations in One Variable

1. Fill in the blank: The graph of a quadratic function f(x) = ax² + bx + c is a symmetrical curve known as a ________.

2. True or False: The x-intercepts of the graph f(x) = ax² + bx + c represent the roots of the equation ax² + bx + c = 0.

3. Solve the quadratic equation x² - 9x + 20 = 0 by factorisation.

4. True or False: If the coefficient 'a' in f(x) = ax² + bx + c is negative, the graph has a minimum point.

5. A farmer wants to enclose a rectangular garden using a wall on one side and 40 metres of fencing for the remaining three sides. (a) If the width of the garden is x metres, express the length in terms of x. (b) Show that the area A m² is given by A = 40x - 2x². (c) Find the maximum area of the garden.

6. The sum of two numbers is 12 and their product is 35. Form a quadratic equation and solve it to find the two numbers.

7. For the function f(x) = -x² + 6x - 8, calculate: (a) the axis of symmetry, (b) the maximum coordinates of the graph.

8. Express the equation (x + 3)(x - 2) = 2x + 4 in the general form ax² + bx + c = 0.

9. Which of the following quadratic functions has a maximum point at (0, 7)?

10. Given the quadratic function f(x) = 2x² - 4x - 6: (a) Determine its y-intercept. (b) Find its x-intercepts. (c) Sketch the graph of f(x).