R.A.T.-Create Your Own Water Park Apply your knowledge of polynomial functions to create a water park,...

R.A.T.-Create Your Own Water Park Apply your knowledge of polynomial functions to create a water park, with 6 waterslides - one for under 6 years old (highest point at least 5m above ground) two for ages 6 to 12 (highest point at least 10m above ground) three for over age 12 (highest point at least 20 m above ground)

A Create a polynomial equation for each waterslide. Show all of your work. The waterslide must begin at the y axis and the x axis must represent the ground. For each function, write the original function in factored form, then explain the transformations that were performed, in order to obtain the model function.

B. Graph (and print) each function using desmos. State the domain and range of each function.

C. Choose one of your waterslides and determine the interval(s) in which the height of the ride was above 3m. Explain your method.

D. Choose one of the waterslides for ages 12 and up and state the interval (from peak to trough) where the waterslide is steepest. Then determine the average rate of change for that interval (by using the equation). Next, determine the instantaneous rate of change at the point in the interval when the person is moving the quickest. Interpret the meaning of these numbers. Note: the maximum steepness of a ride should not exceed 4:1, rise to run. The waterslide should be decelerating as it comes to a stop.

Expert Solution

c) Consider the first case. For height above 3 meter it is certain between interval [0, 3.2]

Colby Messinger answered 2 years ago

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