I am confused about when to use the quadratic equation in the modeling process. Is it possible that the equation is not appropriate for all of the data sets which we use?
You won't always know when to use the quadratic form vs. the power-function form or other forms, and those aren't decisions you'll learn how to make in this class. To make those decisions requires that you know not only how to use the forms but why they arise, which requires more powerful mathematics (e.g., differential equations).
In this class you will learn to use the forms of four the main functions, to use the models to answer questions, and evaluate how well the models work.