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## Solving Quadratic Equations Using the Quadratic Formula

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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.**The Quadratic Formula**The solutions of a quadratic equation written in Standard Form, ax2 + 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**Deriving the Quadratic Formula by Completing the Square.**Divide both sides by “a”. Subtract constant from both sides.**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**Deriving the Quadratic Formula by Completing the Square.**Take the square root of both sides Solve absolute value/ Simplify radical**Deriving the Quadratic Formula by Completing the Square.**Isolate x Simplify Congratulations! You have derived The Quadratic Formula**Graph**Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html**#2 Solve by factoring**This quadratic is Prime (will not factor), The Quadratic Formula must be used!**#2 Solve using the quadratic formula.**Exact Solution Approx Solution**Graph**Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html**#3 Solve using the quadratic formula**The is not a real number, therefore this equation has ‘NO Real Solution’**Graph**Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html**#4 Solve using the quadratic formula**Would factoring work to solve this equation?**Graph**Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html**#5 Solve using the quadratic formula.**Exact Solution Approx Solution**#5 What if we move everything to the right side?**Exact Solution Approx Solution**Graph**Clink on link for graphing calculator. http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html**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.**Understanding the discriminant**Discriminant # of real solutions Perfect square 2 real rational solutions Not Perfect 2 real irrational solutions 1 real rational solution No real solution**#6 Find the discriminant and describe the solutions to the**equations. 2 Real Rational Solutions**#7 Find the discriminant and describe the solutions to the**equations. No Real Solutions**#8 Find the discriminant and describe the solutions to the**equations. 2 Real Irrational Solutions**#9 Find the discriminant and describe the solutions to the**equations. 1 Real Rational Solution