Roller Coaster
Instructions
Parts of a structure in a roller coaster need to be replaced. It is the part between points A and B (see figures below) that needs to be replaced. Your task is to determine two different functions that can be used during construction so that there is a smooth transition in points A and B.
* Use the measurements in the sketch to the right below.
* Use GeoGebra (below) to check if your suggested function formulas are suitable.
* When you are convinced that your function fulfills the required conditions:
- DRAG the function formula into the graphics view (on the right).
* Proceed to the next task!
THE FIRST FUNCTION:
THE SECOND FUNCTION:
GENERALIZATION
Now, try to generalize the results by giving the horizontal distance the value a and the vertical distance the value b.
Use the slider bar tools in the GeoGebra applets below to check your answers for different values of a and b (by dragging the sliders)
The first GENERALIZED function:
The second GENERALIZED function:
If you have time...
Try to find another "unique" function which you think no other group has come up with!
No need for generalization!