Question

The shape of a roller coaster is modeled by a polynomial function, R(x). Describe how to find the x-intercepts of R(x) and how to construct a rough graph of R(x) so that the engineer can predict when there will be no change in the direction of the coaster. You may create a sample polynomial to be used in your explanations.

Answer 1

Can you use calculus?

Answer 2

Which grade are you in?

Answer 3

im in 10th

Answer 4

Learnt calculus yet?

Answer 5

no

Answer 6

I would draw the rough graph by plotting the following points on the graph paper and try to draw a curve between it. If calculus is allowed, it would be much easier.
(0, R(0))
(1, R(1))
(2, R(2))
(3, R(3))
...

If you want more accuracy, use tighter spacing between the points, i.e.
(0, R(0))
(0.5, R(0.5))
(1, R(1))
(1.5, R(1.5))
(2, R(2))
...

There will be no change to the direction of the roller coaster when the tangent of the polynomial is flat.

x-intercept is found by solving R(x)=0