1. The Quadratic Formula and the Discriminant

2. The Discriminant

3. The Discriminant The Discriminant is: Way to solve:
Number and kind of solutions
Positive and Perfect Square
Factor
2 Rational
Zero
1 Rational
Positive not Perfect square
Quadratic formula or Complete the square
2 Irrational
Negative
Don’t solve
No Real Solutions

4. Picture: Positive Discriminant
2 Real Solutions

5. Picture: Zero Discriminant
1 Real Solution

6. Picture: Negative Discriminant
0 Real Solution. 2 Complex Solutions.

7. Using the discriminant

8. Using the discriminant

9. Using the discriminant

10. Using the discriminant

11. If the discriminant is positive and not square alternate complete the square and quadratic formula.