Building Boxes
Polynomial and Rational Functions
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Objective
Students will use the graphing calculator to explore general patterns of polynomial
and rational functions, and a real-world application of a polynomial function.
Overview of the Lesson
In this lesson, students explore relationships between x-intercepts, factors, and roots
of polynomial functions using the graphing calculator. Students also investigate
rational functions, identifying the roots and the asymptotes as well as holes in the
graphs. Students construct boxes of various dimensions using graph paper, collect
height and volume data, and create a scatterplot in order to determine the height of
the box with the maximum volume. Students can solve this problem using a
graphing calculator or by using their own scatterplots drawn by hand. The use of
questioning by the teacher, and the group work of the students are important
features of this lesson.
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