# The BEHEMATH

## Creation of Rollercoaster

Firstly, we came up with a general idea of what we want our roller coaster to look like. We came up with the decision to create a very steep and fast ride. In order to create the roller coaster, we drew a rough sketch of all the polynomial base functions that were required. The functions that we sketched out were linear, polynomial, sinusoidal, quadratic and linear. Once we had a visual of the functions that we could use, we went on google images and searched up blueprints, diagrams and images of famous roller coasters. After looking at the different types of functions used in roller coasters, we matched them up with the functions we had drawn out. Furthermore, we transferred our design onto Desmos and used trial and error and restrictions to create a more precise design. We created the sections of the roller coaster by adding transformations to the base functions we previously looked at. We achieved the steepness of our roller coaster by vertically stretching all the functions. This helped us make a graph with accurate coordinates that fits the time restrictions of 100 seconds.

## Calculations

Solve for the exact time(s) when your rollercoaster reaches a height of:

a) 250 feet

b) 12 feet

2. Calculate average rate of change from:

a) 10 to 15 seconds

b) 50 to 60 seconds

3. Calculate instantaneous rate of change at:

a) 35 seconds