A polynomial function that represents a roller coaster.

[FinnyIsWitty]

The amusement park you are designing for gave you the following coaster requirements:

- your coaster ride must have at least 3-5 relative maxima and/or minima
- the ride length must be at least 4 minutes
- the coaster ride starts at 400 feet
- the ride dives below the ground into a tunnel at least once
- the ride must ‘bounce’ off the ground at least once.

adding a domain and range is allowed.

I am struggling to create a polynomial function that is representative of a roller coaster. Thank-you so much for any help
.

 

[Deleted member 4993]

The amusement park you are designing for gave you the following coaster requirements:

- your coaster ride must have at least 3-5 relative maxima and/or minima
- the ride length must be at least 4 minutes
- the coaster ride starts at 400 feet
- the ride dives below the ground into a tunnel at least once
- the ride must ‘bounce’ off the ground at least once.

adding a domain and range is allowed.

I am struggling to create a polynomial function that is representative of a roller coaster. Thank-you so much for any help
.

What would a function look like if it has one relative maxima and/or minima ?

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[stapel]

The amusement park you are designing for gave you the following coaster requirements:

- your coaster ride must have at least 3-5 relative maxima and/or minima

From your experience with graphing, etc, what must be the minimum degree for, say, a four-critical-point polynomial? So, for however many max/mins you've chosen, what must be the minimum degree of your polynomial? Also, from what you know about what repeated factors do, with respect to max/min points (as opposed to just critical and inflection points), should you have repeated factors?

- the ride length must be at least 4 minutes

So for what must the input variable stand? What input variable have you chosen? What units have you chosen? Minutes? Seconds? Something else? Either way, what is the minimum value for your variable's upper bound?

- the coaster ride starts at 400 feet

So for what must your output variable stand? What output variable have you chosen? What units have you chosen? Meters? Feet? Something else? Either way, when your input variable equals zero, what must be the value of your output variable?

- the ride dives below the ground into a tunnel at least once

So what does this say about the output variable's sign? Does the graph ever cross below the horizontal axis? How many times do you want it to cross below? What does this say about the necessary number of intercepts on the horizontal axis?

- the ride must ‘bounce’ off the ground at least once.

From your graphing experience, when does a graph "bounce" off the horizontal axis? How does this relate to repeated factors? How many times should be factor be repeated? (Hint: Think "even or odd".)

As for the rest, you can make up whatever you like. Not only should you not expect that your answer will match any given classmate's answer, any good grader would strongly suspect that matching answers involved copying. Every student's answer will likely be different!

Please reply with your answers to the above, along with your preliminary thoughts about your polynomial. Thank you!