Question

The change in water level of a lake is modeled by a polynomial function, W(x). Describe...

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 to be used in your explanations.

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Answer #1

Let us create a sample polynomial of cubic order to solve the problem

To find the x-intercepts of the equation, we need to substitute W(x) = y = 0

The values of x obtained after solving the equation are the x-intercepts

To plot the graph, we first need to find the inflection or critical points to see where the graph is changing the concavity

solving the equation will give us the critical points and inflection points, now we can see the points where the graph is increasing and decreasing.

Now find the value of function at all critical points, inflection point, x intecepts and the +,- infinity and plot a smooth graph connecting all the points

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