If you say “quadratic formula”, many people have probably heard of it but do not know what it is used for or what the actual formula is. This lesson will use the formula and discuss how the formula is used to solve problems. The purpose of the quadratic formula is to solve a quadratic equation. It is important to note the distinction between these two. The quadratic formula is a tool. A quadratic equation is usually given to you specifically for the purpose of solving it. When solving a quadratic equation, you are finding the roots of that equation. The roots of the equation will tell you where the graph touches or crosses the x – axis. If you need to know more about quadratic equations or other terminology, click here for an introductory lesson. Many people may be able to memorize the quadratic formula as ^{.} However, you have to know what all those letters mean in order to use the formula properly. The quadratic formula can only be applied to a quadratic equation that is in the standard form of ^{}. If an equation is not in this form, it must be manipulated until it is in standard form  only then can the quadratic formula be applied. 

Whether the solution to the equation is an integer, real number, imaginary or a double root depends on the value under the square root in the quadratic formula The value of is called the discriminant and it determines what type of answer you will get.  When ^{} is a perfect square, you will get rational answers for your solution.
 When the value is not a perfect square, you will get two real number solutions that should be expressed as an exact value rather than a decimal approximation.
 As we said earlier, if ^{} = 0, then you will only get one rational solution. That value will be a double root.
 If the value of ^{} is negative, then you will have two imaginary solutions. In other words, your graph will not touch the x–axis.


