Quadratic Equations is **F**x² + **U**x + **N**

Definition – Quadratic equation is an equation in which the highest power of an unknown quantity is a square. It is a polynomial equation of the second degree.

What does it look like?

A ‘standard’ quadratic equation

**a**x² **+** **b**x **+** **c** = 0

Let’s break it down

- The letters
**a**,**b**and**c**are coefficients (you know those values). They can have any value, except that**a**cannot be 0. [Remember a coefficient is a number before a variable, x is the variable. It is unknown] - The letter “x” is the variable (you don’t know the value as yet)

Here is an example of one:

Give explanation as to why it is called a quadratic equation when it is only raised to the 2^{nd} power. (Hint: word origination)

The solutions to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions to the equation.

They are also called “roots”, or sometimes “zeros”

There are 3 ways to find the solutions:

1) You can factor the Quadratic (find what to multiply to make the Quadratic Equation)

2) You can complete the Square

3) You can use the **Quadratic Formula**:

It is read “minus b plus or minus the square root of b-squared minus four ac, all over two a”

The entire formula can now be explained. The following website gives conceptual information in a fun way.

http://www.coolmath.com/algebra/09-solving-quadratics/05-solving-quadratic-equations-formula-02.htm

http://www.geogebra.org/en/wiki/index.php/Quadratic_Equations

Quadratic Rap – would no longer forget formula

http://www.youtube.com/watch?v=p1Jpdkf2HWY&feature=related

Project and Exercise- use link

http://www.mrbenshoof.com/alg2Documents/Quadratic%20Equations%20Project.pdf

## Using the Quadratic Formula solve the following problem

Just put the values of a, b and c into the quadratic Formula and, do the calculations, also graph the equation.

5x² + 6x+ 1= 0