Birthday Polynomial project for 04/15/2004

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).

Answer 1

We need your birthday to do this assignment correctly.

Let's say the birthday is LEAP YEAR DAY... Feb 29, 2000

then the digits are 02 29 2 0 0 0

the polynomial is then 0x7 +2x^6 + 2x^5 + 9x^4 + 2x^3 + 0x^2 +0x + 0

which simplifies to 2x^6 + 2x^5 + 9x^4 + 2x^3 =

x^3( 2x^3 + 2x^2+ 9x + 2)

the solutions are x=0,0,0, -0.2314, and 2 imaginary/complex solutions

the y-intercept is (0,0)

as x grows to infinity, the polynomial blows up to infinity

as x shrinks to -infinity, the polynomial blows up to infninity

(-1.7) is on the graph so the remainder is 7 when divided by x+1

You now must re do the assignment with YOUR birthday