This module is for Algebra 1, Grades 7-12 Welcome

Mathematics can take on many representations. We can use numbers, letters, graphs, tables and even words to represent mathematical situations. Sometimes one representation is easier to work with than another. Sometimes a specific representation will reveal information that others cannot. In this module, you will work with various representations of quadratic functions to develop an appreciation for each one as you use them to model authentic scenarios.

You will need a graphing calculator to complete this module. Links to instructions for using the TI-83 and TI-84 calculators can be found in the Students Resources section of Teacher Resources.

Module Objectives

By the end of this module, you will be able to:

  • Recognize and write a quadratic function written in three forms: standard, factored, and vertex.
  • Identify the similarities and differences between each of the three forms.
  • Analyze these similarities and differences in relation to a parabola graphed on a coordinate plane.
a double rainbow over a mountain range

The arcs of a rainbow model quadratic functions.


  • Use the zeros of a quadratic function to write the function in factored form.
  • Use the vertex of a quadratic function to write the function in vertex form.
  • Apply algebraic and graphing techniques to write a given quadratic function in standard form, in factored form, and in vertex form.

In this module, the students use the graph of the parabola to find the zeros and the vertex. The students are not factoring to find these values in this module. The purpose of this module is to help students gain an appreciation for the different representations of a quadratic function, and understand the need for factoring and completing the square.