This is the oddest and most hilarious math homework I have ever seen, your teacher is really fun.
The main point is to describe the characteristics instead of "convincing". First plot out the graph, then include everything it says (characteristics) in the flyer. From the "marketing" perspective, think of why a buyer should buy from you instead of other polynomials. This means you should compare the polynomial with others (for example, my polynomial is to the power of 3! x³) and claim that yours is the most special polynomial out there (since you can't compare their "prices")
Your teacher wants you to have fun and be creative, so just cook up some stuff and try to make it sound plausible. Good luck