2. Integrated Math III

3. Essential Question What different methods can be used to solve quadratic equations?

4. Quadratic Formula Quadratic Formula Graphically Click the speaker to hear instructions

5. Solving Quadratics by Factoring Click the calculator to continue…

6. Solving Quadratics using the Quadratic Formula Click the calculator to continue…

7. Solving Quadratics Graphically Click the calculator to continue…

8. Solving Quadratics by Factoring x 2 - 9x + 20 = 0 Click for additional help! (Stapel)

9. Solving Quadratics Graphically x 2 + 4x – 20 = 2 Click for additional help! (Tormoehlen, 2008)

10. 2x 2 -10x – 48 = 0 Solving Quadratics using the Quadratic Formula Click for additional help! ("The quadratic formula," 2007)

11. Here are some helpful hints!  We must first identify our a, b, and c terms.  To factor, we have to find the multiples of c that add up to b.  It is important to remember that a negative times a negative also gives you a positive. Example: If c = 36, the multiples are 36 · 1 -36 · -1 18 · 2 -18 · -2 12 · 3 -12 · -3 6 · 6 -6 · - 6 Click the smiley face to try again… Sorry, your solution is incorrect.

12. Here are some helpful hints!  Once the equation is in factored form, we must remember that it is still equal to zero.  This means that we must set each one of our linear factors equal to zero too.  We then solve for x. Example: (x + 7)(x – 2) = 0 x + 7 = 0 - 7 - 7 x = -7 x - 2 = 0 - 2 -2 x = -2 Click the smiley face to try again… Sorry, your solution is incorrect.

13. Your solution is correct! x 2 - 9x + 20 = 0 (x – 5)(x – 4) = 0 x – 5 = 0x – 4 = 0 + 5 +5 + 4 +4 x = 5x = 4 Click here to continue tutorialhere

14. Here are some helpful hints!  In order to solve quadratics, the equation must be equal to zero.  If not, we have to move all of the terms to one side of the equation. Example: x 2 – 12x + 15 = -8 +8 +8 x 2 – 12x + 23 = 0 Now that the equation is equal to zero, we would be able to graph it and find its solutions. Click the star to try again… Sorry, your solution is incorrect.

15. Click the star to try again… Here are some helpful hints!  In order to solve quadratics, the equation must be equal to zero.  If not, we have to move all of the terms to one side of the equation.  When you bring a positive number over an equals sign, you must perform the opposite operation. Example: x 2 + 8x - 9 = 7 -8 -8 x 2 + 8x - 17 = 0 Now that the equation is equal to zero, we would be able to graph it and find its solutions. Sorry, your solution is incorrect.

16. Your solution is correct! Click here to continue tutorialhere x 2 + 4x – 20 = 2 -2 x 2 + 4x - 22 = 0 We now use our calculator to graph the equation and find its solutions. x = -6x = 2

17. Here are some helpful hints! Click the pencil to try again…  We must first identify our a, b, and c terms.  When plugging the terms into the quadratic formula, we must remember that –b means to change the sign of b. Example: 1 x 2 - 4x - 3 = 0 a b c -4 to +4 Sorry, your solution is incorrect.

18. Here are some helpful hints! Click the pencil to try again…  We need to be careful when using our calculator to simplify the quadratic formula. Example: In our calculator -4 2 is equal to -16. We know that this is not true. A negative squared is always equal to a positive. To fix this mistake, we must insert parenthesis around the negative number. The calculator will then give us the correct solution. Sorry, your solution is incorrect.

19. Click here to continue tutorialhere 2x 2 -10x – 48 = 0 Your solution is correct!

20. Exit Ticket 3 – 2 – 1 Please email me the answers. Write 3 things you liked about this lesson. Write 2 things you learned. Write 1 question you have about solving quadratics. Click here to return to home page.here Click to email Please first click here

21. Resources Stapel, E. (n.d.). Factoring quadratics: the simple case. Retrieved from http://www.purplemath.com/modules/factquad.htm The quadratic formula to solve quadratic equations. (2007). Retrieved from http://www.mathwarehouse.com/quadratic/the-quadratic-formula.php Tormoehlen, T. (Producer). (2008). Solving quadratic equations by graphing. [Web]. Retrieved from http://www.youtube.com/watch?v=8Pk2VN6wzqU