Mrs. Wilson
Algebra II CP
Name:___________________________________________________________________ Block:____________
Polynomial Graph Birthday Project
You are going to create your own personal birthday polynomial!!!!  Use the digits
of the month, day, and 4-digit year of your birth—in order—as the coefficients of the
polynomial. (For example: If your birthday is August 13, 1991, then use the digits
8131991 in that order.) The degree of your polynomial must be a whole number
greater than 2. (Example: 𝑓(𝑥) = 8𝑥 5 − 1𝑥 4 − 3𝑥 3 + 19𝑥 2 − 9𝑥 + 1). Change the
signs of the coefficients to make the most interesting graph you can—one that in
some way reflects you.
1) Create a table of values using synthetic substitution. Neatly write the work on
lined paper as it will be handed in with your project.
2) You will then need to analyze the polynomial by finding the following:
-Degree
-Domain and range
-Describe the end behavior
-All of the zeros (explain how you found them using a table of values – then
use a graphing calculator to get an estimate)
-Relative extrema (explain how you found them using a table of values – then
use a graphing calculator to get an estimate)
3) Create a graph of your polynomial. You can sketch you graph by hand, or use an
online graphing tool, such as Geometer’s Sketchpad (visit the Media Center), or
Desmos graphing calculator (online at https://www.desmos.com/calculator). Print
a screenshot of the graph and then add a title to your graph. Label your x- and yaxes and all zeros and extrema.
4) Write a summary paragraph to explain how many zeros and turning points your
graph could have (theoretically) and how many it actually has. Describe how
Descartes’ rule of signs applies to your polynomial, as well as the relationship
between degree and end behavior. Please use full sentences and appropriate
grammar and punctuation!
Bonus: Make a Presentation of Your Birthday Polynomial on either a nice piece of
paper or poster. Be creative and original. How does the graph of this polynomial
reflect who you are? Present your birthday polynomial neatly, accurately and
artistically.
Due Date: ____________________________________
On this date, you must hand in your:
a) Table and work for synthetic substitution
b) Organizer stating degree, domain, range, etc.
c) graph
d) written summary paragraph
e) rubric
f) the bonus, if you choose to complete it
Each day your project is late, 10 POINTS will be subtracted from the grade!
Name:__________________________________________________________________ Date:____________
Polynomial Graph Birthday Project Rubric
Not Included
(0 points)
Unsatisfactory
(1 points)
Satisfactory
(2 points)
Proficient
(3 points)
Exemplary
(4 points)
Followed
Directions
No polynomial
is written.
Polynomial
follows rules
for coefficients
but not
degrees or vice
versa.
Polynomial
follows rules for
coefficients and
degree.
Polynomial follows
rules for coefficients
and degree, is
written in function
form.
Table of
Values
No table of
values given.
Equation is
written without
regard to
guidelines
regarding
degrees or
coefficients.
Table of values
given, no work
for synthetic
substitution
shown.
Table of values
given, some
work for
synthetic
substitution
shown.
Table of values
given, all work
for synthetic
substitution
shown and
neatly labeled.
Graph of
Function
No graph
provided.
Graph given, no
title or labels on
key features
Graph given,
title given, but
missing a few
key features
Degree and
Zeros
No degree or
real zeros
calculated.
Degree stated, no
real or complex
zeros attempted
Graph given,
no title, but
few key
features
labeled
Degree stated,
real or
complex zeros
attempted, but
all incorrect
Domain and
Range
No domain or
range given.
Either domain or
range given, but
incorrectly.
Both domain
and range
given. Both
incorrect.
Both domain
and range given.
One incorrect
Table of values given
and correct, all work
for synthetic
substitution shown
and neatly labeled.
Zeros and extrema
labeled.
Graph given, axes
labeled, titled, and all
zeros and extrema
labeled with
coordinates.
Degree stated, zeros
stated correctly,
classification given
based on degree, and
number of complex
zeros stated
correctly with
justification.
Both domain and
range given. Both
correct.
End Behavior
No end
behavior given.
End behavior
stated, one
part incorrect.
Extrema
No extrema
given.
End behavior
attempted,
neither part
correct.
1 extrema
stated, incorrect.
Analysis
No analysis
attempted.
Analysis
attempted, but
not all aspects
included. Not in
paragraph form
Analysis
attempted but
not all aspects
included. 1 – 2
sentences.
End behavior
stated correctly,
but not using
proper notation.
All extrema
stated, incorrect
in value or
classification of
relative and
absolute
Analysis
attempted. All
aspects
included. In
paragraph form.
2 extrema
stated,
incorrect.
Degree stated,
real zeros
stated correctly
and number of
complex zeros
stated, some
correct
Total Points from Rubric: __________________________ x 2 = ______________________
_______ points for handing in at beginning of block on due date with rubric.
End behavior stated
correctly using
proper notation.
All extrema stated
correctly, correct
classification of
relative and
absolute.
Thorough analysis
provided. All aspects
included. Thorough
summary provided
in paragraph form
with comment on
Descartes’ Rule of
signs.
Name:__________________________________________________________________ Date:____________
Polynomial Function:
Table of Values:
x
Degree/Classification
End Behavior:
Zeros
Extrema:
f(x)
Domain/Range