Birthday Polynomial 3st4f

Name __________________________________________________

Foundations of Math 3 – Birthday & Artistic Polynomial Rubric The goal of this project is to creatively demonstrate your knowledge of polynomial characteristics. Due September 30th I. Your Birthday Polynomial Construct your birthday polynomial as follows: B(x) = x3 – (month) x2 + (day) x – (year) For example, if your birth date is March 31, 1985, then B(x) = x3 - 3x2 + 31x – 85.

My birthday polynomial is B(x) = _________________________________ Part 1: Use Excel to graph your birthday polynomial and to answer all of the following questions. Use your graphing calculator to analyze the graph and answer the following questions. Enter B(x) into y1. Find a window that gives a good view of B(x), including its roots and y-intercept. State the window used on your Excel report page.

1. Birthday Polynomial B(x) = ___________________________________ 2. List the Real roots (x-intercepts) ____________________ 3. List the y-intercept(s) __________ 4. Domain ___________________ 5. Range_____________________ 6. Relative maximum__________________ 7. Relative minimum___________________ 8. Find B(2) = _________ 9. Is B(x) increasing or decreasing at x = 2? ____________

Part 2: Pick one root (Note: You may have only one Real root.) Call it R. R = __________ Do not round off R when you find the root and store it in R in the calculator.

Divide

B( x) ( x  R) .

1. Write the Quotient here. Q (x) = ____________________________ Note: There should be no remainder. (Or almost no remainder…. not to round off the Root, and it should come out without a remainder.) 2. Graph the quadratic polynomial Q(x). 3. Find its vertex. Call that point (H, K). Store the values of H and K, again without rounding them off. H = __________

K = _________

Now find the following. Do round off these answers to 3 decimal places. 4. 2 H + R = ________________________

5. H2 + K + 2 R*H = __________________

6. R*(H2 + K) = _____________________ What do you notice?

Part 3:

Round answers to the nearest thousandth.

1) My polynomial B(x) = _______________________________________________

2) Find B(4) = _____ Is your function increasing, decreasing, or neither as it es through this point? ______________ 3) Find B(-2) = _____ Is your function increasing, decreasing, or neither as it es through this point? ______________ 4) Is B(x) a one-to-one function? _____ Why? ________________________________________ 5) Find B(-x) = ___________________________________________________ Is B(x) even, odd, or neither? ____________ Why? ____________________________________________ 6) Find B(2x) = ___________________________________________________ Is this transformation a horizontal stretch or a horizontal shrink? __________ 7) How many solutions will this equation have? If |B(x)| = 10 __________ 8) True or False? B(x) will always have the same exact roots as B(-x)._______ 9) True or False? B(x) will always have the same exact roots as –B(x)._______ 10)

True or False? B(x) will always have the same exact roots as B|(x)|._____

11)

True or False? B(x) will always have the same exact roots as |B(x)|._____

12)

True or False? If B(x) is an nth degree polynomial, then it has n Real roots (although some of them may be repeats). ________

Part 4: Create a unique artistic drawing that uses at least 6 of the following 12 Birthday Polynomial transformations listed below as the center piece of your design. B(x) + # B(x) - # B(#x) B (x/#) # B(x) B(x) / # B(x + #) B(x - #) -B(x) B(-x) |B(x)| B|x| 20 pts 15 pts 15 pts 20 pts 20 pts 10 pts 100 pts

Part 1 (Excel & Graphing Calculator Usage) Part 2 Part 3 Part 4 (Summary about the finished design) Creativity, Neatness, Design, & Presentation Promptness & Neatness (10 pts = on time or 10 pts off for each day late) Sept 30th Total Possible Points