Quadratic Functions: Understanding the Different Representations of Parabolas

Joshua Krajci and Dr. Ivona Grzegorczyk


We explore the different ways of how quadratic functions are represented through equations, graphs, and tables. In order for mathematics students to get a deep understanding of how quadratic functions work, we must understand the advantages and disadvantages of each of the quadratic function representations, which are the standard form, vertex form, and factored form. Different methods of algebraic manipulation, such as factoring and completing the square, will be utilized. Furthermore, we explore how these functions can be represented on a graph, and then see how transformations affect the quadratic function. These various representations, methods, and topics are valuable for any mathematics student who is taking any form of an algebra course, as quadratic functions are used in future math courses, as well as in other types of school subjects such as Physics and Business Mathematics. By understanding the different representations of a quadratic function, as well as how it can be transformed, and then applied into different fields, will be very useful for education purposes.


  1. Congratulations Joshua!

    Education research is so important — were you able to test your theory on students? I liked the rocket example.

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