1. 1 Aims Introduce Quadratic Formulae. Objectives Identify how to solve quadratic equation’s using a quadratic equation.

2. Multiplying out brackets Brackets can be removed from an expression by multiplying out brackets e.g. (x + 5)(x + 7) = x 2 + 7x + 5x + 35 = x 2 + 12x + 35 This give a quadratic expression. A quadratic expression looks like ax 2 + bx + c where a, b and c are numbers and a must not equal 0. x+5 x +7 x2x2 + 5x + 7x + 35

3. The Quadratic Equation! Used to solve an equation in the form: ax 2 + bx + c = 0

4. x 2 + x - 2 = 0 a= 1, b = 1, c = -2 x = 1 or -2

5. 2x 2 + 5x - 3 = 0 a= 2, b = 5, c = -3 x = -3 or 0.5

6. Solve the quadratic equation 3x² + 9x+4 = 0 Here a = 3, b = 9 and c = 4. Putting these values into the quadratic formula gives

7. Solve the quadratic equation 8x² + 3x − 4 = 0. Care is needed here because the value of c is negative, that is c = −4.

8. Find the roots of the following quadratic equations: a)x² + 6x − 8 = 0, b)2x² − 8x − 3 = 0, c)-3x² + x+1 = 0.

9. A cyclist takes (x – 21) hours to travel a distance of 46 kilometres when cycling at an average speed of x kilometres. Find the cyclist average speed? Distance = Speed x Time 46 = x(x-21) 46 =x² - 21