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Question 1207554: Using Desmos calculator design a roller coaster.
• use only quadratic functions
• create one full loop
• start and end your roller coaster slightly a above the ground level (x-axes will
indicate the ground level)
• make at least one "function" below the ground level
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! To create a roller coaster on Desmos using only quadratic functions, we'll need to piece together multiple functions, each defining a specific section of the track. Here's a basic outline:
Initial Climb: A quadratic function that starts at ground level and rises to a peak.
First Drop: A quadratic function that descends from the peak, going below ground level.
Loop: Two quadratic functions, one for the upward part of the loop and one for the downward part.
Final Drop and Leveling Off: A quadratic function that descends from the loop and levels off slightly above ground level.
Here's a possible set of equations:
f(x) = -0.05(x-10)^2 + 10 // Initial climb
g(x) = -0.1(x-20)^2 + 15 // First drop
h(x) = 0.05(x-30)^2 - 5 // Upward part of the loop
i(x) = -0.05(x-40)^2 + 5 // Downward part of the loop
j(x) = -0.02(x-50)^2 + 1 // Final drop and leveling off
To input these functions into Desmos:
Go to https://www.desmos.com/calculator
In the expression bar, type each function one by one, pressing Enter after each.
You can adjust the coefficients to fine-tune the shape of the roller coaster. For example, increasing the coefficient of the squared term will make the curve steeper, while decreasing it will make it flatter.
Remember to experiment and have fun! You can create more complex roller coasters by adding more functions and adjusting the parameters.
Tip: To visualize the roller coaster better, you can adjust the viewing window in Desmos. Click on the wrench icon in the top right corner and adjust the x-min, x-max, y-min, and y-max values.
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