1. 1.) 2.) Algebra 2/Trigonometry Name: __________________________
6.6 Worksheet Date: ________________ Block: _____
For each polynomial, complete the following:
(a) Use the Leading Coefficient Test to describe the end behavior.
(b) Use your graphing calculator to locate one of the zeros. Then, find all remaining Zeros. All non- integer zeros must be written as improper fractions. You must show all work & checks for these!
(c) Write the polynomial in factored form.
(d) Sketch the graph of the polynomial. (You must include the y-intercept, all zeros, any relative minima/maxima, and the basic shape using the Leading Coefficient Test).
1.)
𝑓 𝑥 = 𝑥 3 −4 𝑥 2 −𝑥+4
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________
(d) Relative Minima/Maxima: _________________________________________________________
2.)
𝑓 𝑥 = 𝑥 3 −7𝑥−6
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________
(d) Relative Minima/Maxima: _________________________________________________________

2. Note: you may need to change the scale on the y-axis.
For each polynomial, complete the following:
(a) Use the Leading Coefficient Test to describe the end behavior.
(b) Use your graphing calculator to locate one of the zeros. Then, find all remaining Zeros. All non- integer zeros must be written as improper fractions. You must show all work & checks for these!
(c) Write the polynomial in factored form.
(d) Sketch the graph of the polynomial. (You must include the y-intercept, all zeros, any relative minima/maxima, and the basic shape using the Leading Coefficient Test).
3.)
𝑓 𝑥 =− 𝑥 3 +6 𝑥 2 −11𝑥+6
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________
(d) Relative Minima/Maxima: _________________________________________________________
4.)
𝑓 𝑥 =2 𝑥 4 −15 𝑥 𝑥 2 +15𝑥−25
Note: you may need to change the scale on the y-axis.
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________
(d) Relative Minima/Maxima: _________________________________________________________

3. 5.) 6.) 𝑓 𝑥 = 𝑥 3 −3 𝑥 2 +𝑥−3 𝑓 𝑥 = 𝑥 3 + 𝑥 2 +9𝑥+9
For each polynomial, complete the following:
(a) Use the Leading Coefficient Test to describe the end behavior.
(b) Use your graphing calculator to locate one of the zeros. Then, find all remaining Zeros. All non- integer zeros must be written as improper fractions. You must show all work & checks for these!
(c) Write the polynomial in factored form.
(d) Sketch the graph of the polynomial. (You must include the y-intercept, all zeros, any relative minima/maxima, and the basic shape using the Leading Coefficient Test).
5.)
𝑓 𝑥 = 𝑥 3 −3 𝑥 2 +𝑥−3
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Factored Form: ____________________________________
(d) Relative Minima/Maxima: _________________________________________________________
6.)
𝑓 𝑥 = 𝑥 3 + 𝑥 2 +9𝑥+9
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Factored Form: ____________________________________
(d) Relative Minima/Maxima: _________________________________________________________

4. Note: you should change the scale on the y-axis.
For each polynomial, complete the following:
(a) Use the Leading Coefficient Test to describe the end behavior.
(b) Use your graphing calculator to locate one of the zeros. Then, find all remaining Zeros. All non- integer zeros must be written as improper fractions. You must show all work & checks for these!
(c) Write the polynomial in factored form.
(d) Sketch the graph of the polynomial. (You must include the y-intercept, all zeros, any relative minima/maxima, and the basic shape using the Leading Coefficient Test).
7.)
𝑓 𝑥 = 3𝑥 3 −19 𝑥 2 +33𝑥−9
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________
(d) Relative Minima/Maxima: _________________________________________________________
8.)
𝑓 𝑥 = − 𝑥 4 +5𝑥 3 +3 𝑥 2 −17𝑥+10
Note: you should change the scale on the y-axis.
(a) Describe End Behavior: ______________________________________________________
(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________
(d) Relative Minima/Maxima: _________________________________________________________