1. Lesson 1-6 Solving Quadratic Equations

2. Objective:

3. To solve quadratic equations using different methods.

4. Quadratic Equation:

5. Any equation that can be written in ax 2 + bx + c = 0 form.

6. Three methods for solving quadratic equations:

7. 1)Factoring.

8. Three methods for solving quadratic equations: 1)Factoring. 2)Completing the square.

9. Three methods for solving quadratic equations: 1)Factoring. 2)Completing the square. 3)Quadratic formula.

10. Solve by factoring:

11. Solve by completing the square:

12. Solve by using the Quadratic Formula:

13. Quadratic Formula:

14. The discriminant is the expression which is under the radical.

15. Quadratic Formula: The discriminant is the expression which is under the radical. The discriminant tells us something special about the roots (x- intercepts) and the solutions (roots and zeros).

16. Quadratic Formula:

17. If there will exist 2 complex conjugate roots.

18. Quadratic Formula: If there will exist 2 complex conjugate roots. If there will exist 1 real root called a double root.

19. Quadratic Formula: If there will exist 2 complex conjugate roots. If there will exist 1 real root called a double root. If there will exist 2 distinct real roots.

20. Helpful Hints when Solving Equations:

21. If a, b, and c are integers, and if b 2 - 4ac is a perfect square, then factor.

22. Helpful Hints when Solving Equations:

23. If neither of those two cases work, then use the quadratic formula.

24. Two Special Circumstances to Look For:

25. Losing a Root

26. Two Special Circumstances to Look For: Losing a Root Gaining a Root

27. Losing a Root:

28. Gaining a Root: (Check for Extraneous Roots)

29. Assignment: Pgs. 34-35 C.E.  1-19 all, W.E.  1-19 odd