One night, a guy named Kevin walked into a Casino begging to play one of the poker tables. Kevin had made bets with his friends, had lost, and was now in massive amounts of debt.

The Casino decides to play with Kevin for a little. They decided to try to teach Kevin a lesson on gambling. The Casino models the amount of money Kevin will have or owe via the function:

f(x)=-x^5+15x^4-66x^3+80x^2

Wheref(x) represents the amount of money in thousands and,x, represents time in hours.

Answer the following questions about Kevin's soon-to-be loss in the Casino.

Questions

1. Predict what the graph will look like, and explain how you know it would look as such. Focus on type of function and end behavior.

1. When will Kevin break even? Please find all factors and zeros of this function and show your work.
2. What is another method in which you could have determined when Kevin will have zero money in his account besides factoring?
3. What do the negative time values represent? Are they valid in this situation?

1. What is the domain and range of the function? Assume the Casino kicks Kevin out when he loses $1 000 000.

1. Sketch the polynomial over the correct domain. Is it close to your prediction?

1. What will happen after 8 hours of playing at the Casino? When do they kick Kevin out?