Birthday Polynomial for 11/11/2004

Question

1. Identify IN ORDER the digits of the month (1 or 2 digits), day (1 or 2 digits), and year (4 digits) of your birthday.

For example, if I was born on November 22, 1985, my ordered birthday digits would be “11221985.” (The most number of digits you could have is 8, and the least number of digits you could have is 3).

2. Create a polynomial using your digits in order.

Again, for example, my polynomial could be y = x7 + x6 + 2x5 + 2x4 + x3 + 9x2 + 8x + 5

3. Using https://www.desmos.com/calculator, graph your birthday polynomial. Experiment with the shape of your birthday polynomial by changing the signs of your various terms. Try to create a polynomial function with an interesting shape and some turning points. Be creative!

4. Analyze your polynomial by finding these characteristics:

· List the y-intercept. (Can be found using desmos)

· List all x-intercepts. (Can be found using desmos)

· Describe the end behavior of your polynomial (as x, f(x)?, and as x-, f(x)?)).

· Divide your polynomial by (x – 1) using synthetic division (show all work). Is (x – 1) a factor of your polynomial?

· Evaluate your polynomial for x = -1 (Show all work).

1. An X-Y Table with at least 10 points
2. ● All Zeros (listed and labeled on graph)
3. ● Y-intercept (listed and labeled on graph)
4. ● Relative maximum and minimums (listed and labeled on graph)
5. ● A sentence description of end behavior and why it occurs.

Answer 1

In writing your birthday as 11/11/2004, you've done most of the work for part 1 (Just remove the slashes.) For part 2, remember that when 1 is a coefficient, it gets hidden. (y = x7 + x6 + 2x5 + 2x4 + x3 + 9x2 + 8x + 5 is secretly y = 1x7 + 1x6 + 2x5 + 2x4 + 1x3 + 9x2 + 8x + 5.)

How far along this process are you able to get?