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.) 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: ____________________________________________________________

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: ____________________________________________________________

**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: ____________________________________________________________

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: ____________________________________________________________

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: ____________________________________________________________