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

First. Finding the x-intercepts of   Let  be the change in water level. So to find the x-intercepts of this function we can use The Rational Zero Test that states: To find the zeros of the polynomial: We use the Trial-and-Error Method which states that a factor of the constant term: can be a zero of a polynomial (the x-intercepts). So let's use an example: Suppose you have the following polynomial: where the constant term is . The possible zeros are the factors of this term, that is: . Thus: From the foregoing, we can affirm that  are zeros of the polynomial. Second. Construction a rough graph of   Given that this is a polynomial, then the function is continuous. To graph it we set the roots on the coordinate system. We take the interval: and compute  where  is a real number between -2 and -1. If , the curve start rising, if not, the curve start falling. For instance: Therefore the curve start falling and it goes up and down until  and from this point it rises without a bound as shown in the figure below