You have decided to become a structural engineer who specializes in roller coaster design. Your job is to design a section of your next roller coaster based on a 4th degree polynomial. The amusement park you are designing for has the following requirements. ~ Your polynomial will have the x-axis placed even with the boarding terminal

~ Your polynomial will have 3 roots

~ The ride will pass through the x-axis twice (multiplicity of one at these roots)

~ The ride will touch the x-axis once and turn around (multiplicity of 2 at this root)