1. 3.4 – The Quadratic Formula

2. Deriving The Formula Quadratic equation standard form
Subtract c from both sides
Divide both sides by a
Complete the square
Simplify
Square root both sides
Subtract from both sides
Simplify

3. Example 1

4. Example 2

5. Example 3

6. The Discriminant Two imaginary solutions One real solution
Two real solutions

7. Example 4
Because the discriminant is greater than zero, the equation has two real solutions.

8. Example 5
If the discriminant is 0, there’s one real solution.

9. Example 6
The ball is in the air for seconds.