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 that the meteorologist can predict when there will be no change in water vapor. you may create a sample polynomial to be used in your explanation.

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 that  the meteorologist can predict when there will be no change in water vapor.  you may create a sample polynomial to be used in your explanation.

anonymous · Answer

please help!!

ranga · Answer

X-intercept of a polynomial c(x) is found by setting c(x) = 0 and solving for x.
This is same as finding the roots or zeros of the polynomial because a root or a zero is the value of x that makes the function become zero.

anonymous · Answer

so what are they asking for me to answer?

anonymous · Answer

im really confused

ranga · Answer

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.

anonymous · Answer

oh i see

ranga · Answer

Draw a rough graph.  
The polynomial we created is a parabola.
Since its x-intercepts are 2 and 3, the graph will cross the x axis at x = 2 and x = 3
Since the leading coefficient x^2 - 5x + 6 is positive, it is a parabola that will open upward.
The rough graph will look like this:

ranga · Answer

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ranga · Answer

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.

That is all.

anonymous · Answer

hmm i think i get it man wow thanks

anonymous · Answer

i have one more little question @ranga

anonymous · Answer

ok nevermind i figured it out