First, here is the existing map of current structures. It is important that the rollercoaster does not go through the foundation of any of these structures.

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your rollercoaster. Show all of your work.
@mathmale

Question

First, here is the existing map of current structures. It is important that the rollercoaster does not go through the foundation of any of these structures.

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your rollercoaster. Show all of your work.
@mathmale

mathmale · Answer

Howdy, @DI_KAZ !

Looks as though neither you nor your graph ever crashes through the roller coaster foundation.

However, you do touch the foundation at 3 different x-values:  {-7,-2,6}.  Hope you're well padded to avoid injury.

Those x-values are called "roots" of the polynomial in question.

The root -7 becomes the factor (x+7); -2 => (x+2); and 6=> (x-6).
Multiply any two of these factors together and simplify the result.  Then mult. that result by the remaining factor; the result will the the polynomial you wanted!

While I have to and will get off the Internet now, I'll look for your response later.

Best of luck.  Mathmale