Understanding the properties and methods to solve quadratic equations is essential for to the student to advance in Algebra. This chapter explains each concept in a very specific and focused manner. After students have been introduced to quadratic equations they build up their knowledge by learning various techniques to solve them. Additionally, they will learn the connection between solutions and graphs of quadratic functions. Methods and procedures are applied to graph quadratic inequalities and solve word problems. Lastly the chapter covers complex and imaginary numbers. Students are introduced to complex number operations, graphs and the role complex and imaginary numbers have as solutions to equations.