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**First.** <u>Finding the x-intercepts of </u>

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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:

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From the foregoing, we can affirm that

are zeros of the polynomial.

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**Second.** <u>Construction a rough graph of</u>

** **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