**Formula** of Quadratic Equations

A quadratic equation is an equation that can be written as:

ax ² + bx + c where a ≠ 0

A quadratic equation must have a squared term as its highest power

**Examples** of Quadratic Equations

- y = 2x² + 3x + 7
- y = 13x² + 2
- y = x² − 4x + 15
- y = −x² + 5

**Examples** of Equations that are *NOT* Quadratic

- y = 11x + 223
- y = x
^{3}− 4x² +5x +6 - y = 2x
^{3}− 7x² - y = −x
^{4}+ 5

The solution of a quadratic equation is the value of x when you set the equation equal to zero

i.e. When you solve the following general equation:0 = ax² + bx + c

Given a quadratic equation:ax ² + bx + c

One method to solve the equation for zero is to factor the equations.

### General Steps to solve by factoring

Create a factor chart for all factor pairs of c

A factor pair is just two numbers that multiply and give you c

- Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b
Note: if the pair does not exist, you must either complete the square or use the quadratic formula.

- Insert the pair you found in step 2 into two binomals

Solve each binomial for zero to get the solutions of the quadratic equation.

**Example** of how to solve a quadratic equation by factoring

Quadratic Equation: y = x² + 2x + 1

Below is a picture representing the graph of y = x² + 2x + 1

as well as the solution we found by factoringBelow is a picture of the graph of the quadrtaic y = x² − 2x + 1

as well as the solutionsBelow is a picture of the graph of the quadrtaic y = x² − 2x + 1 as well as the solutions

y = x² − 4x − 4

is graphed below as well as its solution (2,0)xy = x² + 6x + 9

is graphed below as well as its solution (2,0)y = x² + 2x − 3

is graphed below as well as both the solutionsy = x² − 2x − 3

is graphed below as well as both the solutions