6.5 The Quadratic Formula and the Discriminant

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Presentation transcript:

6.5 The Quadratic Formula and the Discriminant

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

The Quadratic Formula Solve for x by completing the square.

The Quadratic Formula Solve for x by completing the square.

The Quadratic Formula Solve for x by completing the square.

The Quadratic Formula Solve for x by completing the square.

Yes, you can remember this formula Pop goes the Weasel http://www.youtube.com/watch?v=2lbABbfU6Zc&feature=related Gilligan’s Island http://www.youtube.com/watch?v=3CWTt9QFioY&feature=related This one I can’t explain http://www.youtube.com/watch?v=haq6kpWdEMs&feature=related

How does it work Equation:

How does it work Equation:

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

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 ).

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.

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

Solve using the Quadratic formula

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

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

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

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

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

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

Homework Page 318 # 15 – 39 odd

Homework Page 318 # 14 – 38 even # 61 - 66