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.
2 answers:
The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.
Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.
Let the polynomial function be c(x) = x ² -7x + 10
To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:
x ² -7x + 10 = 0
Factorizing the middle term, we get:
x ² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) =0
(x - 2)(x - 5)=0
x - 2 = 0 ⇒ x=2
x - 5 = 0 ⇒ x=5
Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.
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fund-raising project. The cost of paint color needed is php 1,200 plus php 45 each pot. She estimates that your class will design 80 pots and sell designed pots for php 100 each.
Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spac
