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Solving Quadratic Equations Using the Quadratic Formula MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring and by using the quadratic formula.

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The Quadratic Formula The solutions of a quadratic equation written in Standard Form, ax 2 + bx + c = 0, can be found by Using the Quadratic Formula. Click on the link below to view a song to help you memorize it. http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadsongs.htm

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Deriving the Quadratic Formula by Completing the Square. Divide both sides by “a”. Subtract constant from both sides.

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Deriving the Quadratic Formula by Completing the Square. Complete The Square Factor the Perfect Square Trinomial Simplify expression on the left side by finding the LCD

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Deriving the Quadratic Formula by Completing the Square. Take the square root of both sides Solve absolute value/ Simplify radical

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Deriving the Quadratic Formula by Completing the Square. Isolate x Simplify Congratulations! You have derived The Quadratic Formula

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#1 Solve using the quadratic formula.

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Graph Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

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#1 Solve by factoring

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#2 Solve by factoring This quadratic is Prime (will not factor), The Quadratic Formula must be used!

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#2 Solve using the quadratic formula. Exact Solution Approx Solution

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Graph Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

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#3 Solve using the quadratic formula The is not a real number, therefore this equation has ‘ NO Real Solution ’

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Graph Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

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#4 Solve using the quadratic formula Would factoring work to solve this equation?

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Graph Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

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#5 Solve using the quadratic formula. Exact Solution Approx Solution

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#5 What if we move everything to the right side? Exact Solution Approx Solution

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Graph Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

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The Discriminant The expression inside the radical in the quadratic formula is called the Discriminant. The discriminant can be used to determine the number of solutions that a quadratic has.

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Understanding the discriminant Discriminant # of real solutions 1 real rational solution No real solution Perfect square Not Perfect 2 real rational solutions 2 real irrational solutions

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#6 Find the discriminant and describe the solutions to the equations. 2 Real Rational Solutions

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#7 Find the discriminant and describe the solutions to the equations. No Real Solutions

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#8 Find the discriminant and describe the solutions to the equations. 2 Real Irrational Solutions

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#9 Find the discriminant and describe the solutions to the equations. 1 Real Rational Solution

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