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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/
© 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.
© Boardworks 2012 3 of 9 Information
© 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
© Boardworks 2012 5 of 9 Completing the square
© Boardworks 2012 6 of 9 Using the quadratic formula
© 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
© Boardworks 2012 8 of 9 Using b 2 – 4 ac
© Boardworks 2012 9 of 9
Finding Complex Roots of Quadratics
What are you finding when you solve the quadratic formula? Where the graph crosses the x-axis Also known as: Zeros, Roots and X-intercepts.
solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.
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Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =
7.1 – Completing the Square
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Objectives: To solve quadratic equations using the Quadratic Formula. To determine the number of solutions by using the discriminant.
Section 10.5 – Page 506 Objectives Use the quadratic formula to find solutions to quadratic equations. Use the quadratic formula to find the zeros of a.
© Boardworks of 8 The Equation of a Straight Line To enable the animations and activities in this presentation, Flash Player needs to be installed.
Goals: To solve quadratic equations by using the Quadratic Formula.
Exploring Quadratic Functions and Inequalities
Algebra 1B Chapter 9 Solving Quadratic Equations By Graphing.
Algebra 9.5 Solving Quadratic Equations Using the Quadratic Formula This is an important section as there are many questions on the STAR test about the.
The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)
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