Polynomial Analysis Homework Packet

Complete polynomial analysis including end behavior description, locating zeros, finding y-intercepts, factoring, and sketching graphs for given polynomials in a homework packet. Utilize the leading coefficient test and graphing calculator to identify zeros and graph features accurately.

• Polynomial Analysis
• End Behavior
• Zeros
• Graphing Calculator
• Factoring

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1. Algebra 2/Trigonometry 6.6 Homework Packet Name: __________________________ 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! (You do NOT have to check imaginary zeros) (c) Identify the y-intercept of the graph. (d) Write the polynomial in factored form. (e) 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). Use this scale: x-axis one block = y-axis one block = 1 1.) ? ? = ?3 4?2 ? + 4 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________ 2.) Use this scale: x-axis one block = y-axis one block = 1 ? ? = ?3 7? 6 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________

2. 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! (You do NOT have to check imaginary zeros) (c) Identify the y-intercept of the graph. (d) Write the polynomial in factored form. (e) 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.) Use this scale: x-axis one block = y-axis one block = 1 ? ? = ?3+ 6?2 11? + 6 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________ 4.) Use this scale: x-axis one block = y-axis one block = 4 ? ? = 2?4 15?3+ 23?2+ 15? 25 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________

3. 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! (You do NOT have to check imaginary zeros) (c) Identify the y-intercept of the graph. (d) Write the polynomial in factored form. (e) 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.) Use this scale: x-axis one block = y-axis one block = 1 ? ? = ?3 3?2+ ? 3 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________ 6.) Use this scale: x-axis one block = y-axis one block = 2 ? ? = ?3+ ?2+ 9? + 9 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________

4. 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! (You do NOT have to check imaginary zeros) (c) Identify the y-intercept of the graph. (d) Write the polynomial in factored form. (e) 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.) Use this scale: x-axis one block = y-axis one block = 1 ? ? = 3?3+ 19?2 33? + 9 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________ 8.) ? ? = ?4+ 5?3+ 3?2 17? + 10 Use this scale: x-axis one block = y-axis one block = 5 (a) Describe End Behavior: As x , ________. And as x - , ________. (b) Zeros: ___________________________ (c) y-intercept: _________ (d) Product of Linear Factors: ____________________________________________________________ (e) Relative Minima/Maxima: _____________________________________________________________