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: _________________________________________________________

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 3 +23 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: _________________________________________________________

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: _________________________________________________________

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: _________________________________________________________