I need to do a birthday polynomial project my birthday is December 3, 2004 and I currently do not understand how to do the project .

Answer 1

I found reference to Birthday Polynomial Project at:

chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.chino.k12.ca.us/cms/lib8/CA01902308/Centricity/Domain/2515/Polynomial%20PROJECT%20birthdaygraph.pdf

Write, 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, April 2, 1976 could be “421976” or “4021976”. Use must use 6, 7 or 8 digits.

Analyze your polynomial (using your calculator) by finding these characteristics:

a. Roots (x-intercepts)

b. Y-intercept

c. Relative minimums and maximums

d. End behavior

e. Points (x, y)

Your code could be: 12032004, and the polynomial could be:

f(x) = x⁷ + 2x⁶ - 3x⁴ + 2x³ + 4 (notice the coefficient of 0 drops out 3 terms)

You should plot this on Desmos to see the shape and the fact it has only one real root.

I changed the sign of the third term so that x = -1 is the real root:

f(-1) = (-1)⁷ + 2(-1)⁶ - 3(-1)⁴ + 2(-1)³ + 4

f(-1) = -1 + 2 - 3 +2 + 4

f(-1) = 0

This would be the answer to "a". (Note all other 6 roots are complex and are not real.)

The y-intercept is found by substituting x = 0 into the polynomial:

f(x) = x⁷ + 2x⁶ - 3x⁴ + 2x³ + 4

f(0) = 4

This would be the answer to "b".

Inspecting the graph shows it really does not have any relative minimums or maximums. If you chnage the signs for some the terms this will change.

This would be the answer to "c".

On the left the function values increases from -∞ to 4, on the right the function value increases from 4 to +∞.

This would be the answer to "d".

I leave it to you to generate some points by substituting values of x into the function definition to get their associated f(x) values.

Answer 2

12032004

f(x)=x⁷+2x⁶-3x⁴-2x³+4

4 was added to "parent" so graph is moved up 4.

domain and range are both (-infinity, infinity)

when x=0 the y intercept is 4.

As for y=0, you will need to graph, the polynomial is unfactorable. If it were factorable then x=+/-1, or +/-2, or +/-4 would be factor and on graph y=0 at about x= -1.5

min/max can also be determined from graph.