# Quadratic Relations

### Expanding, Factoring, Solving, & Completing the Square

## PART I: Expanding

Expanding is simple as long as you follow the rules of BEDMAS (Brackets, Exponents, Division/Multiplication, and Addition/Subtraction).

When expanding, you need to make sure that you always "break" or "open" the brackets.

To do so you must always take note that there is always a number outside the bracket. This number must be multiplied to every term in the bracket.

## PART II: Factoring

## Factoring by Simple Trinomials (Product and Sum)

## Factoring Complex Trinomials (Decomposition)

## PART III: Solving Quadratic Relations (Solving for "X")

There are 3 ways to solve for "x". One method would be to factor the equation and solve for the "x" while the second method would be to plug the equation into the quadratic formula. A quadratic equation can consist of a maximum of two x-intercepts (roots) or a minimum of no x-intercepts (roots). The last method, would be by graphing however, the other two methods stated before would be much more efficient.

## Solve by Factoring The easiest way to solve for "x" is by factoring. After factoring the equation, you simply solve for "x" by solving for each term individually. | ## Solve using Quadratic Formula The quadratic formula is used to solve for "x" when the equation is unfactorable or when the numbers are too big to factor. NOTE: If the number under the square root is a NEGATIVE number, the quadratic question does not have x-intercepts. | ## Solving by Graphing Although graphing can be used to find your x-intercepts, it would prove to be insufficient and slow as compared to the others that are faster and exact. |

## Solve by Factoring

## Solve using Quadratic Formula

NOTE: If the number under the square root is a NEGATIVE number, the quadratic question does not have x-intercepts.