This week in Pre Calc 11 we learnt three different methods on how to solve Quadratic Equations. The first method is Factoring, it is the fastest and the easiest method and there are two differnt ways that you can factor a Quatratic Equation. The first one is the Grouping Method which is the one that I prefer or the second one is the Box Method, which is a much more visual way to factor the equations. When factoring using the Grouping Method the first step is to determine which two numbers can multiply to the third term and add to the second term. For example, in the equation you have to find two numbers that multiply to and two numbers that add to Those two numbers would be  and  From there, you can determine what the two factors of the first equation would be:  Once you have found the factors you can then solve for  In order to solve for  you must first isolate it.     which mean that  and 

The second method that we learned is Completing the Square. This method can be used to solve any Quadratic Equation especially those that can not be solved by factoring. When Completing the Square of a Quadratic Equation you can first verify that the equation is not factorable, for example: is not factorable because there are not two numbers that multiply to and add to which means that you can use the Completing the Square method. Once you have verified that the equation is not factorable, you can then rewrite the equation leaving space to add in your zero pairs: b = zero pairs. Ex:  To find the zero pairs, you divide the middle number by two and then you square it. Ex:  and  Once you have your completed equation, which includes the zero pairs,  you can factor the first three terms and since the last two terms are like terms you can combine and simplify them as well. Ex:  You are now solving to isolate  which means you would add  to both sides of the equation. Ex:  From there you square root both sides. Ex: Next you subtract  from both sides to give you your final answer. Ex: 

The third method that we learned is the Quadratic Formula. This method can also be used to solve any Quadratic Equation but it is a little more complex and there are more steps, leaving you more opportunities to make a mistake. To start you have to determine which numbers are a, b and c and then from there you can put the numbers into to formula to easily solve the equation.

I have included an example below that shows the detailed steps I would take to solve a Quadratic Equation using the Quadratic Formula.