Boardworks of 8 The quadratic formula To enable the animations and activities in this presentation, Flash Player needs to be installed. This can be downloaded free of charge from Boardworks of 8 Information Boardworks of 8 Any quadratic equation of the form ax 2 + bx + c = 0 can be solved by substituting the values of a, b and c into the formula: x = b b 2 4 ac 2a2a This equation can be derived by completing the square on the general form of the quadratic equation. The quadratic formula Boardworks of 8 Completing the square Boardworks of 8 Using the quadratic formula Boardworks of 8 The roots of a graph We can demonstrate each of these possibilities using graphs. Remember, if we plot the graph of y = ax 2 + bx + c, the solutions to the equation ax 2 + bx + c = 0 are given by the points where the graph crosses the x -axis. y x b 2 4 ac is zero one solution y x b 2 4 ac is negative no real solution y x b 2 4 ac is positive two solutions Boardworks of 8 Using b 2 4 ac Boardworks of 8