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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.

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Presentation on theme: "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."— Presentation transcript:

1 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.

2 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

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

4 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

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

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

7 #1 Solve using the quadratic formula.

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

9 #1 Solve by factoring

10 #2 Solve by factoring This quadratic is Prime (will not factor), The Quadratic Formula must be used!

11 #2 Solve using the quadratic formula. Exact Solution Approx Solution

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

13 #3 Solve using the quadratic formula The is not a real number, therefore this equation has ‘ NO Real Solution ’

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

15 #4 Solve using the quadratic formula Would factoring work to solve this equation?

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

17 #5 Solve using the quadratic formula. Exact Solution Approx Solution

18 #5 What if we move everything to the right side? Exact Solution Approx Solution

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

20 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.

21 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

22 #6 Find the discriminant and describe the solutions to the equations. 2 Real Rational Solutions

23 #7 Find the discriminant and describe the solutions to the equations. No Real Solutions

24 #8 Find the discriminant and describe the solutions to the equations. 2 Real Irrational Solutions

25 #9 Find the discriminant and describe the solutions to the equations. 1 Real Rational Solution

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