1. 1.) Algebra 2/Trigonometry Name: ________________
Section 6.6 Notes – Graphing Polynomial Functions Date: _________________
Finding the zeros of polynomial functions of third degree or higher:
**Rational Root Test OR:
Graph ___________ on a Graphing Calculator
Find where the graph crosses the __________ (These are the ________ ________)
Verify the _________ using ____________ __________________
Repeat this process until you are left with a _______________
Factor the __________ or use the ______________ formula to find the remaining __________
Steps to Graph a Polynomial Function with ALL REAL ZEROS:
1.) Identify the _____________ __________________
2.) Find the ______________________
3.) Find the ______________________
4.) Estimate the relative _________________ & _________________ values
5.) Sketch the Graph
For each of the examples, write f(x) as a product of linear factors and list all of its zeros. Then sketch the graph.
1.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ Y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

2. 2.) 3.) Algebra 2/Trigonometry
Section 6.6 Notes – Graphing Polynomial Functions
For each of the examples today, write f(x) as a product of linear factors and list all of its zeros. Then sketch the graph.
2.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ Y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
3.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ Y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

3. 4.) 5.) Algebra 2/Trigonometry
Section 6.6 Notes – Graphing Polynomial Functions
For each of the examples today, write f(x) as a product of linear factors and list all of its zeros. Then sketch the graph.
4.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ Y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
5.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ Y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

4. **x-intercept becomes a _____________ ________________**
Algebra 2/Trigonometry Name: __________________________
Section 6.6 Notes Day 2 Date: _______________ Block: _____
If a function has a repeated zero, what is the effect on the graph?
If the factor (x-a) is repeated an __________ number of times:
_________________________________________________________
**x-intercept becomes a _____________ ________________**
If the factor (x-a) is repeated an __________ number of times:
_________________________________________________________
1.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
2.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

5. 3.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
Recall: Polynomials can have at most n x-intercepts (where n is the degree of the polynomial).
4.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Factored Form: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

6. Algebra 2/Trigonometry
Section 6.6 Notes – Day 2
5.)
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________