1. Section 2.5 – Quadratic Equations

2. Quadratics Solving Quadratics Factoring Square Root Method
A quadratic equation is an equation that can be written in the form where a, b, and c are real numbers and
Examples:
Solving
Quadratics
Factoring
Square Root Method
Completing the Square
Quadratic Formula

3. Solve by Factoring
Zero Product Principle: If , then a = 0 or b = 0.

4. Square Root Method
If then

5. Solve by Completing the Square
1 – Leading coefficient must be 1.
Divide thorough by leading coefficient.
2 – Move constant to the right side.
3 – Find
Add to both sides.
4 – Factor on the left, simplify on the right.
5 – Take the Square Root of both sides.
6 – Simplify square roots = Right side simplifies with
7 – Solve for the variable.

6. Solve by Completing the Square
Side work:

7. Quadratic Formula

8. Quadratic Formula
Ex.

9. The Discriminant
The discriminant is the expression under the radical in the quadratic formula.
Two imaginary solutions – complex conjugates
One real solution
Two distinct real solutions

10. The Discriminant
Ex.
Since the discriminant is negative, we will have two complex solutions that are complex conjugates.
This means that the graph has NO x-intercepts.