1. 6.5 The Quadratic Formula and the Discriminant

2. We have a number of different way of finding the roots if a quadratic equations
#1. Making a table
#2. Factoring
#3. Completing the Square
Now a new way that comes from completing the square.
The Quadratic Formula

3. The Quadratic Formula
Solve for x by completing the square.

4. The Quadratic Formula
Solve for x by completing the square.

5. The Quadratic Formula
Solve for x by completing the square.

6. The Quadratic Formula
Solve for x by completing the square.

7. Yes, you can remember this formula
Pop goes the Weasel
Gilligan’s Island
This one I can’t explain

8. How does it work
Equation:

9. How does it work
Equation:

10. The Discriminant
The number in the square root of the quadratic formula.

11. The Discriminant The Discriminant can be negative, positive or zero
If the Discriminant is positive,
there are 2 real answers.
If the square root is not a prefect square
( for example ),
then there will be 2 irrational roots
( for example ).

12. The Discriminant The Discriminant can be negative, positive or zero
If the Discriminant is positive,
there are 2 real answers.
If the Discriminant is zero,
there is 1 real answer.
If the Discriminant is negative,
there are 2 complex answers.
complex answer have i.

13. Solve using the Quadratic formula

14. Solve using the Quadratic formula

15. Solve using the Quadratic formula

16. Solve using the Quadratic formula

17. Solve using the Quadratic formula

18. Solve using the Quadratic formula

19. Solve using the Quadratic formula

20. Solve using the Quadratic formula

21. Solve using the Quadratic formula

22. Solve using the Quadratic formula

23. Solve using the Quadratic formula

24. Describe the roots
Tell me the Discriminant and the type of roots

25. Describe the roots 0, One rational root
Tell me the Discriminant and the type of roots
0, One rational root

26. Describe the roots 0, One rational root
Tell me the Discriminant and the type of roots
0, One rational root

27. Describe the roots 0, One rational root -11, Two complex roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots

28. Describe the roots 0, One rational root -11, Two complex roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots

29. Describe the roots 0, One rational root -11, Two complex roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots
80, Two irrational roots

30. Homework
Page 318
# 15 – 39 odd

31. Homework
Page 318
# 14 – 38 even #