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Describing Graphs of Polynomial Functions

We want to sketch the graph of a polynomial function. Let's think about what the given information tells us.

Let's begin by plotting the intercepts. Recall that the intercepts are the zeros of the function.

For simplicity, we will sketch the graph of the function with only three real zeros. While we are drawing the curve that passes through the zeros, we should remember that the graph has a local maximum at and local minimums at and

Note that this is only one of the infinitely many graphs with the given characteristics. Any graph with zeros at and a maximum at and minimums at and will be correct.