Welcome to Unit 3!
Do the following:
 Do the warm-up in composition notebbok
 Pick up papers from the front whiteboard
Warm-up (do in composition notebooks)
 On whiteboard
HW #1:
• P 208 #15-23 odd, 24
• Make notecards from U3L1 (definition one side and
vocab. word on the other side)
Agenda
 U3L1: Polynomial Functions
Learning Objective(s)
By the end of this period you will be able to:
Our goal for this section is for you to be able to sketch a polynomial
function.
Notes
You are going to take notes in your composition notebook. I will
have the vocabulary on the powerpoint slides
Take them in any way that you learn best ( Cornell notes, etc)
Polynomial Functions (4.1)
Polynomial
o Created from one or more terms.
• Terms are numbers and variables separated by an addition
sign.
• Example: g(x) = 5x + 2x2 – 3
5x, 2x2, and -3 are terms
o Must have non-negative whole number exponents!
Example:
Non-Example:
Polynomial Functions (4.1)
Standard Form of a Polynomial
o Written with the highest exponent to lowest exponent
• Example: x5 + 4x3 – 3x
5 is the highest degree, 3 is the
next highest, and then 1 is the
lowest.
Degree of a Polynomial
o The highest exponent in a polynomial.
o Example: x5 + 4x3 – 3x
5 is the degree of the polynomial.
Polynomial Functions (4.1)
Leading Term
o Term with the highest exponent
• Example: x5 + 4x3 – 3x
x5 is the leading term.
Constant Term
o Term without a variable
Example: x5 + 4x3 – 3x -9
-9 is the constant term.
On your notes, write down “See Example #1 and 2 on 3.1
worksheet”
Whiteboards!
Identify if the equation is a polynomial. IF the equation is a
polynomial identify: (1) Degree, (2) Leading Term, and (3) Write it in
Standard Form.
Polynomial Functions (4.1)
In your notebook, create a polynomial in standard form and identify
the leading term and degree. Create a second equation; this
equation is NOT a polynomial. Provide one sentence stating why
your equation is not a polynomial.
Polynomial Functions (4.1)
Find 2 other students in the room. You must choose a student who
has:
(1) A name starting with the same letter as yours.
(2) A last name starting with the same letter as yours.
These people CANNOT be at your table!
You will be checking your partners work. If a student see a mistake in
your work they are to help correct your mistake. Your partner must
print their name on your notes.
Polynomial Functions (4.1)
Now attempt Example 1 and 2 on your worksheet
Polynomial Functions (4.1)
Write this in your composition notebook
What are Zeros? (Roots or x-intercepts)
o When f(x) = 0.
o They are the solutions to a polynomial.
o When it intersects the x-axis
o EX) f(x) = x(x-8)(x+9)
Polynomial Functions (4.1)
How to determine if a graph is going to touch (bounce off) x-axis
or cross it?
o For a graph to cross the x-axis:
o The factor has an odd multiplicity
o For a graph to touch the x-axis:
o The factor has an even multiplicity
Example ( on notes)
State the x-intercepts and their multiplicity and whether
the graph touches or crosses x-axis. Also , state yintercept
Example 3
Now let’s do Example 3 on your worksheet!!!!
Polynomial Functions (4.1)
Turning Points
o The number of maxima, minima, or curvature changes.
o If the degree of a polynomial is n, then the graph has at most (n-1)
turning points
o To find the degree of a polynomial it is the number of turning
points plus 1.
Example
Example 4
Now let’s do Example 4 on your worksheet!!!!
Polynomial Functions (4.1)
End Behavior
o Describes the start and end of a graph
o Identify using leading term
Polynomial Functions (4.1)
Polynomial Functions (4.1)
How to Write End Behavior?
Whiteboard
Identify the end behavior.
a. P(x) = -2x5 + 3x2 – 4x – 1
b. S(x) = 3x2 + x + 1
Example 5
Now let’s do Example 5 on your worksheet!!!!
Sketching a Graph
Now we are going to put everything together that we learned
today 
Ex: Sketching a Graph:
a. List the degree and number of turning points
b. State the end behavior
c. Find the y-intercept of the graph
d. Find the x-intercepts of the graph and state whether the
graph crosses ( goes through) or touches( bounces) at
those points
e. Based on your information, sketch a quick graph
Example 7
Now attempt Example 7 on your worksheet
Write a Polynomial Function from its Graph
Step 1: Use roots; put in factored form
Write a Polynomial Function from its Graph
Step 2: Use pt ( x, y) to find a
You cannot use a zero!
Example 8
Now attempt Example 8 on your worksheet
Cool-Down…
I am going to randomly ask questions based on todays lesson and I
will randomly call on you to answer them. You may reference notes,
but please try not too.
Exit Ticket
What did you prefer better? Writing all the definitions and how to
do the problems in your composition notebook and doing example
problems on your worksheet OR having everything in the same
packet?