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

@iwanttogotostanford

Answer 2

ok! i can help :-)

Answer 3

so:
To find the x-intercept of C(x), we start by setting the equation ( C(x) ) to be equal to zero and then we solve for x. This can also be applied to any polynomial to find the x-intercept.

Answer 4

To find the x-intercept of C(x), we start by setting the equation ( C(x) ) to be equal to zero and then we solve for x. This can also be applied to any polynomial to find the x-intercept. For example C(x) = x^3-x. Setting this equal to 0 and solving gives the x intercepts x=0,-1,1. So the graph cuts the x axis at x=0,-1,1.

A rough graph can be sketched by using x intercepts and the end bahavior. The degree of C(x) is odd and the leading coefficient is positive so the graph goes DOWN and UP on ends.

Answer 5

so basically : They want you to create a sample polynomial.

You can pick the roots beforehand and that will make creating the polynomial easier.

Just let us pick x = 2 and x = 3 as the roots or zeros.
That means (x-2) and (x-3) are factors of the polynomial.
Multiply them out and you will create the sample polynomial.
c(x) = (x-2)(x-3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6
c(x) = x^2 - 5x + 6 is the sample polynomial.

Find the x-intercepts for this polynomial.
x-intercepts is same as the roots/zeros of the polynomial and is found by setting x(x) = 0 and solving for x.
x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x-3) - 2(x-3) = 0
(x-2)(x-3) = 0
x = 2 or 3. Therefore the x-intercepts are 2 and 3.

Answer 6

The change in water vapor at any x is found by the slope of the graph at that x.
No change in water vapor means the slope is zero.
That happens at the vertex of the parabola where the tangent will be horizontal.

Answer 7

sorry that was ALOT but this problem took a lot of explaining haha!

Answer 8

Thank you!!

Answer 9

For any help with spanish just tag me.

Answer 10

ok thanks!!!:-)