*Instructional Unit*

*Graphing Polynomials*

* *

**Background**: My choice of mathematical content came
from my teaching of Algebra II in the past few years. One particular chapter from the textbook that we used in
that class was devoted to the study of polynomials. Some of the topics covered in the chapter were the addition,
subtraction, and multiplication of polynomials. My focus in this instructional unit is on other topics covered
in that chapter: the solving of roots, end behavior, and an introduction to
relative extrema.

**Objectives
Addressed in these Lessons (from Georgia Performance Standards for Accelerated
Mathematics 2):**

á
Investigate and explain characteristics
of exponential functions, including domain and range, asymptotes, zeros,
intercepts, intervals of increase and decrease, rates of change, and end
behavior. (MA2A1b)

á
Understand the effects of the
following on the graph of a polynomial function: degree, lead coefficient, and
multiplicity of real zeros.
(MA2A3b)

á
Investigate and explain
characteristics of polynomial functions, including domain and range,
intercepts, zeros, relative and absolute extrema, intervals of increase and
decrease, and end behavior. (MA2A3d)

á
Find real and complex roots
of higher degree polynomial equations using the factor theorem, remainder
theorem, rational root theorem, and fundamental theorem of algebra,
incorporating complex and radical conjugates. (MA2A5a)

á
Solve polynomial,
exponential, and logarithmic equations analytically, graphically, and using
appropriate technology. (MA2A5b)

**Lessons from the
Instructional Unit (and Suggested Class Time. I believe these times would be based on 50-minute class periods. It might be the case that lessons here
be presented in a different order.)**

** **

Lesson #1: End
Behavior (2 classes)

Lesson #2: DescartesŐ Rule of Signs (2 classes)

Lesson #3:
Introduction to Fundamental Theorem of Algebra (2 classes)

Lesson #4:
Investigation on Roots of Polynomials (2 classes)

Lesson #5:
Introduction to Relative Extrema (2 classes)