Toothpicks and Transformations
Quadratic Functions
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Objective
Students will investigate quadratic functions using geometric toothpick designs.
Overview of the Lesson
The lesson begins with a review of transformations of quadratic functions—vertical
and horizontal shifts, and stretches and shrinks. First, students match the symbolic
form of the function to the appropriate graph, then given the graphs, students
analyze the various transformations and determine the equation for the functions.
This review is followed by an activity where students explore a mathematical pattern
that emerges as they build a geometric design with toothpicks. The pattern is
quadratic, and the students determine the mathematical model in several different
forms. Students examine the recursive nature of the relationship. An explicit model
for the relation is developed, and a third model is developed by examining the
scatterplot and determining the equation from the transformations. Finally, the class
uses the graphing calculators to develop another model and to verify that all of the
models&151;factored form, vertex form, and general form&151;are equivalent.
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