# Roller-coaster Summative: N.A.R.A

## The Key to Success

Some difficulties we had as a group when making our roller coaster was agreeing on how we wanted the ride to look, as well as being able to contribute all the required equations in our roller coaster. At first, we drew a basic outline and wrote the general equations for all seven necessary functions and then brainstormed on how our roller coaster would look like. Since the roller coaster had to run from zero to one hundred seconds, we initially decided to have a total of eight equations and have each equation run for 12.5 seconds, which would make up the whole ride. We soon realized that this would not work and then decided to first just agree on how we would like our roller coaster to look like and incorporate all the equations into it later. Once we all finally agreed on the desired look, our new problem was to make sure that all equations were being incorporated into it. We also had some difficulties with the restrictions for the polynomial function since, we had to make restrictions for both the domain and range while, for other equations it was just the domain. It took some time, but using the method of guess and check, we were able to create the roller coaster, which, we all agreed upon, and was also able to incorporate all seven functions.

## The Report

In general, the distance of our graph increases as time increases. More specifically, however:

- during intervals (0,3.3), (77.5, 89), and (96.3, 100) seconds, distance stays consistent

- during intervals (3.31, 9), (30, 45), (47.27, 50), (53.55, 56.695), (65, 77.5), and (89, 93) seconds, the distance decreases

- during intervals (9, 30), (45, 47.27), (50, 53.55), (56.69, 65), and (93, 96.3) seconds, the distance increases