Topics: Quadratic functions, completing the square
Overview: In this activity students will use a novel way of interpreting “completing the square” to explore the family of linear functions that complete the square for various trinomials (i.e., square completers) and the relationship of these functions to the original (i.e., seed) trinomial. Part 1 will use Virtual Algebra Tiles and graphing calculators. Subsequent part(s) will use dynamic geometry software.
Connections to core curriculum: High School - Algebra, A-REI 4: Use the method of completing the square to transform any quadratic equation in x into an equation of the form that has the same solutions. Derive the quadratic formula from this form. High School – Functions, F-IF 8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
Objectives:
• Students will use virtual algebra tiles to investigate different ways to “complete the square”.
• Students will derive a general formula for the family of “square completers” for a specific trinomial and for a generalized trinomial.
• Students will investigate the graphical relationship between seed trinomials, square completers, and completed squared trinomials.
