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© Boardworks 2012 1 of 9 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 http://get.adobe.com/flashplayer/http://get.adobe.com/flashplayer/

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© Boardworks 2012 2 of 9 This sample is an excerpt from one presentation on The Quadratic Formula in Boardworks High School Algebra I, which contains 57 interactive presentations in total.

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© Boardworks 2012 3 of 9 Information

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© Boardworks 2012 4 of 9 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

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© Boardworks 2012 5 of 9 Completing the square

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© Boardworks 2012 6 of 9 Using the quadratic formula

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© Boardworks 2012 7 of 9 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

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© Boardworks 2012 8 of 9 Using b 2 – 4 ac

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© Boardworks 2012 9 of 9

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