Ride the Polynomial: Roller Coaster Curves and Calculations Cont.

After the quick thrill of the smaller bump, we approach the heart of our roller coaster – a complex middle section with multiple twists and turns. Here, the polynomial function becomes more intricate, reflecting the sophisticated design required to balance excitement with safety. We’ll need to graph this function to visualize the coaster’s path and ensure that each twist contributes to the ride’s overall thrill factor.

The middle section of the coaster, with various hills and valleys, is modeled by the polynomial function [latex]j(x)=−x^4+6x^3−9x^2+4x[/latex].

As we leave the middle section, we approach the grand finale of our roller coaster. This final feature is designed to leave a lasting impression, combining the thrill of a steep drop with the safety of leveling out before the ride’s end. The polynomial function here must encapsulate this duality. Let’s examine the end behavior of this function to ensure it delivers an exhilarating yet secure conclusion to our roller coaster adventure.

The last feature of the ride, a sudden drop followed by a smooth finish, is modeled by the polynomial function [latex]k(x)=−2x^3+9x^2−12x+7[/latex].

By completing these tasks, Jordan can confidently present a roller coaster design that is mathematically sound, thrilling, and safe. This activity showcases the application of polynomial functions in engineering, emphasizing their role in creating complex and enjoyable experiences. Terrific work today!