1. Using the Quadratic Formula to Solve Quadratic Equations
Section 9.6
Using the Quadratic Formula to Solve Quadratic Equations

2. Formula
The solutions of the quadratic equation are given by the quadratic formula:

3. Quadratic Formula Common Error
The Quadratic Formula
Quadratic Formula Common Error
Warning
Solve
Example

4. Solving by Using the Quadratic Formula
Solution

5. Solving by Using the Quadratic Formula
Example
Solve
Write in the form
Solution

6. Write in the form Solution:
The Quadratic Formula
Solving by Using the Quadratic Formula
Solution Continued
Write in the form
Solution:

7. Solving by Using the Quadratic Formula
Example
Solve
Solution

8. Solving by Using the Quadratic Formula
Solution Continued
Example

9. Example Solution Solve
Solving a Quadratic Equation That Has Imaginary-Number Solutions
Solving by Using the Quadratic Formula
Example
Solve
Solution

10. Determining the Number of Real-Number Solution
Determining the Number and Type of Solutions
Process
For the quadratic equation , the discriminant is
Also,
• If b2 − 4ac > 0, there are two real-number solutions
• If b2 − 4ac = 0, there is one real-number solution
• If b2 −4ac < 0, there are two imaginary-number solutions (and no real-number solutions)