Algebra II

Polynomial Functions in Roller Coasters

The roller coaster pictured to the left is the Great American Scream Machine. In the outlined portion of the track, I labeled each hump and some key features. The zeros in this portion are -3 and 2. The relative minimum is -3, and the absolute and relative maximum is 3. The Y-intercept is -3. The function changes intervals to go from increasing to decreasing multiple times, forming 3 humps. The end behavior of the left end of the function (x to negative infinity) is infinitely decreasing, and the end behavior of the right end (x to positive infinity) is also infinitely decreasing. I now know this coaster's polynomial function has an exponent of 6, because of the amount of humps it has doubled, and I also know it has to be even because both end behaviors are going in the same direction. I know the leading coefficient is negative because both end behaviors are decreasing. Polynomial functions can be seen in the design of many roller coasters because the coasters have a minimum and maximum point, just like a graphed function. The ending behaviors and amount of humps/loops in the design determine the exponents and leading sign in a function.