𝑓 (𝑥 )=𝑥3−4 𝑥2−𝑥+4

𝑓 (𝑥 )=𝑥3−7 𝑥−6

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.)

2.)

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________

(d) Relative Minima/Maxima: _________________________________________________________

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________

(d) Relative Minima/Maxima: _________________________________________________________

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.)

4.)

𝑓 (𝑥 )=−𝑥3+6 𝑥2−11𝑥+6

𝑓 (𝑥 )=2𝑥4−15 𝑥3+23 𝑥2+15𝑥−25Note: you may

need to change the

scale on the y-axis.

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________

(d) Relative Minima/Maxima: _________________________________________________________

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________

(d) Relative Minima/Maxima: _________________________________________________________

𝑓 (𝑥 )=𝑥3−3 𝑥2+𝑥−3

𝑓 (𝑥 )=𝑥3+𝑥2+9 𝑥+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.)

6.)

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Factored Form: ____________________________________

(d) Relative Minima/Maxima: _________________________________________________________

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Factored Form: ____________________________________

(d) Relative Minima/Maxima: _________________________________________________________

𝑓 (𝑥 )=3 𝑥3−19 𝑥2+33𝑥−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).7.)

8.)

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________

(d) Relative Minima/Maxima: _________________________________________________________

(a) Describe End Behavior: As x , ________. And as x -, ________.

(b) Zeros: ___________________ (c) Product of Linear Factors: ____________________________

(d) Relative Minima/Maxima: _________________________________________________________

𝑓 (𝑥 )=−𝑥4+5 𝑥3+3 𝑥2−17 𝑥+10Note: you

should change the scale on the y-axis.