1. Solving quadratic equations Factorisation Type 1: No constant term Solve x 2 – 6x = 0 x (x – 6) = 0 x = 0 or x – 6 = 0 Solutions: x = 0 or x = 6 Graph of y = x 2 – 6x y x x = 3 (0, 0) (6, 0) y = x 2 – 6x Vertex(3, -9)

2. Solving quadratic equations Factorisation Type 2: No linear term Solve x 2 – 9 = 0 x 2 – 9 = x 2 – 3 2 (x + 3)(x – 3) = 0 Solutions: x = -3 or x = 3 Graph of y = x 2 – 9 y x x = 0 (-3, 0) (3, 0) y = x 2 – 9 Vertex(0, -9) Difference of two squares = (x + 3)(x – 3) x + 3 = 0 or x – 3 = 0

3. Solving quadratic equations Factorisation Type 3: All three terms Solve x 2 – x – 12 = 0 x 2 – x – 12 = a  b = -12 and a + b = -1 Solutions: x = -3 or x = 4 Graph of y = x 2 – x - 12 y x x = ½ (-3, 0) (4, 0) y = x 2 – x -12 Vertex( ½, -12 ¼ ) (x )(x ) (x + 3)(x – 4) = 0 a = 3 and b = -4 x + 3 = 0 or x – 4 = 0

4. Factorise the following quadratic equations hence solve them. 1.3x 2 – 2x = 0 x(3x – 2) = 0 x = 0 or 3x – 2 = 0 x = 0 or x = 2 / 3 2.4x 2 – 5 = 0 (2x +  5)(2x -  5) = 0 2x +  5 = 0 or Difference of two squares 2x -  5 = 0 or 3.x 2 + 2x = 8 x 2 + 2x – 8 = 0 (x + 4)(x – 2) = 0 x + 4 = 0 or x – 2 = 0 4.5x 2 + 13x - 6 = 0 (5x - 2)(x + 3) = 0 5x – 2 = 0 or x + 3 = 0 x = - 4 or x = 2 x = 2 / 5 or x = - 3