B. Analyzing Quadratic Functions Expressed in Standard Form

In Lesson 2.1, you worked with quadratic functions expressed, almost exclusively, in standard form and their graphs. You also saw that the location and shape of the parabola changed as the equation of the function changed.

Now you will explore the role of each term, and more importantly, the role of each coefficient, in graphing a quadratic function given in the form . And, from your work in Lesson 2.1, you may find that some of these roles are familiar.

It is helpful to understand the impact the coefficient of each term has on the graph of a quadratic function before considering the standard form of a quadratic function as a whole.

Open the Quadratic Function applet(5 February 2013, Created with GeoGebra). Move the sliders to change the a, b, and c values. Try changing each value, while leaving the other two constant to determine the effect of each individual parameter. The table below may help you to organize your thinking.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


Parameter Effect on the Graph
Changing a

Changing b

Changing c