Question

The change in water vapor in a cloud is modeled by a polynomial function, C(x). Describe how to find the x-intercepts of C(x) and how to construct a rough graph of C(x) so that the meteorologist can predict when there will be no change in the water vapor. You may create a sample polynomial of degree 3 or higher to use in your explanations.

Answer 1

how to find x-intercepts: plug in C(x) = 0 and solve for x

how to construct a rough graph: plot the x intercepts, look at the degree (highest exponent term), subtract 1, that's how many "turns" of the graph there are. check the sign of the leading coefficient, that will give you the end behavior.