Question

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The change in the water level of a water tower is modeled by a polynomial function, W(x) = -5x^3 + 7x - 2. Which components of the equation relay information on the end behavior of the graph and describe the end behavior of the graph. Describe how many x-intercepts of W(x) can be found and which components of the equation relays that information. Using graphing technology find the approximate x-intercepts so that the city Water Department can predict when there will be no change in the water level

Answer 1

Solution-

The change in the water level of a water tower is modeled by a polynomial function,

$w(x)=-5x^3+7x-2$

The end behavior of a graph is defined as what is going on at the ends of each graph or in which direction are the ends of the graphs heading.

It can be predicted by the leading coefficient and the degree of the polynomial.

Leading coefficient of w(x) = -5

Degree of w(x) = 3

We know that,

When degree is odd and leading coefficient is negative, then graph rises to the left and falls to the right

.

x-intercept of function is where the value of y=0 or where the graph intersects the x-axis. This point also represents the roots or zeros.

As the number of roots is equal to the degree of the polynomial. As the polynomial is a 3 degree polynomial, so it has 3 roots or 3 x-intercepts.

Plotting the graph, the x-intercepts were found to be -1.306, 1, 0.306 . So at these points the water level will be 0.