Algebra II Name:___________________________________________________________________ Block:____________ Polynomial Graph Birthday Project You are going to create your own personal birthday polynomial!!!!  Use the digits of the month, day, and 4-­‐digit year of your birth—in order—as the coefficients of the polynomial. (For example: If your birthday is August 3, 1991, then use the digits 831991 in that order.) The degree of your polynomial must be a whole number greater than five and must include at least three possible positive real zeros (look back at Descartes’ Rule of Signs). (Example: 𝑓 𝑥 = 8𝑥 ! − 3𝑥 ! + 𝑥 ! + 9𝑥 ! − 9𝑥 + 1). PART 1 Create your polynomial and a table of values. Be sure to include enough values that would help you analyze your graph and includes all zeros and extrema, along with the end behavior, within in the table. Due Date: ____________________________________ _________________________________________________________________________________________________________________________________________________ PART 2 You will then need to analyze the polynomial by finding the following: a) Degree b) Domain and range c) Describe the end behavior d) Chart for possible positive real zeros, possible negative real zeros, and possible imaginary zeros e) All of the real zeros (explain how you can find them using a table of values – then use a graphing calculator to get an estimate) and identify how many imaginary zeros there are f) Extrema Due Date: ____________________________________ _________________________________________________________________________________________________________________________________________________ PART 3 Create a graph of your polynomial. Sketch you graph by hand (with help from the calculator) on graph paper. Label your x-­‐ and y-­‐axes and all zeros and extrema. Be sure to title your graph. Due Date: ____________________________________ Each day your project is late, 2 POINTS will be subtracted from the grade! Name:________________________________________________________________ Date:____________ Polynomial Graph Birthday Project Rubric PART 1 Birthday: Polynomial Function: Table of Values: x f(x) PART 1 RUBRIC Not Included Unsatisfactory (0 points) (1 points) Satisfactory (2 points) Polynomial Function No polynomial is written. Polynomial Polynomial follows rules follows rules for for coefficients coefficients and but not degree. degrees or vice versa. Polynomial follows rules for coefficients and degree, is written in function form. Table of Values No table of values given. Table of values given, but only includes two of the extrema or zeros. Table of values is given and includes all of the extrema or zeros. Equation is written without regard to guidelines regarding degrees or coefficients. Table of values given, but only includes one of the extrema or zeros. Proficient (3 points) Table of values is given, but only includes a few of the extrema or zeros. Exemplary (4 points) Name:__________________________________________________________________ Date:____________ Polynomial Graph Birthday Project Rubric PART 2 a) Degree/Classification c) End Behavior: d) Possible Zeros Chart: e) Zeros (real and # of imaginary): f) Extrema: b) Domain/Range PART 2 RUBRIC Not Included Unsatisfactory (0 points) (1 points) Satisfactory (2 points) Proficient (3 points) Exemplary (4 points) Degree (a) and Zeros (e) No degrees stated, no real zeros calculated, or no mention of complex zeros. Degree stated, no real zeros or number of complex zeros stated. Degree stated, real zeros calculated and correct but no mention of complex zeros. Degree stated, real and complex zeros stated correctly. Domain and Range (b) No domain or range given. Either domain or range given, but incorrectly. End Behavior (c) No end behavior given. Both domain and range given. Both incorrect. End behavior stated, one part incorrect. Degree stated, real zeros stated correctly and number of complex zeros stated incorrectly. Both domain and range given. One incorrect End behavior End behavior attempted, stated correctly, neither part but not using correct. proper notation. No chart given. Chart created by Chart given but Chart given but no sign changes two of the one of the were couted columns is columns is correctly. incorrect. incorrect. No extrema 1 extrema stated, 2 extrema All extrema given. incorrect in stated, stated, incorrect value or incorrect in in value or classification of value or classification of relative and classification relative and absolute. of relative and absolute. absolute. End behavior stated correctly using proper notation. Chart is correct for all three columns. Possible Zeros Chart (d) Extrema (f) Both domain and range given. Both correct. All extrema stated correctly, correct classification of relative and absolute. Name:__________________________________________________________________ Date:____________ Polynomial Graph Birthday Project Rubric PART 3 RUBRIC Graph of Function Not Included Unsatisfactory (0 points) (1 points) No graph provided. Graph given, no title or labels on key features Satisfactory (2 points) Proficient (3 points) Exemplary (4 points) Graph given, no title, but few key features labeled Graph given, title given, but missing a few key features Graph given, axes labeled, titled, and all zeros and extrema labeled with coordinates.