1. 4.8 The Quadratic Formula and the Discriminant

2. 2 Real Solutions

3. 1 Real Solution

4. 0 Real Solution.
2 Complex Solutions.
(Imaginary)

5. 2 Real Solutions

6. 1 Real Solution

7. 0 Real Solution. 2 Complex Solutions.
(Imaginary)

8. 2 Real Solutions
1 Real Solution
0 Real Solutions;
2 complex solutions
is called the Discriminant.

9. The Quadratic Formula Starting with any quadratic equation:
We could solve it by completing the square and develop a formula that could be used to solve any quadratic equation.
Here is the solution to the quadratic equation above:
We will call this the Quadratic Formula. Memorize it.

10. Solve this quadratic equation using the quadratic formula: