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

- The graph of $p(x)$ has zeros, $x-$intercepts, at $x=-3,$ $x=1,$ and $x=5.$
- $p(x)$ has a relative maximum value when $x=1.$
- $p(x)$ has a relative minimum value when $x=-2$ and when $x=4.$

Let's begin by plotting the $x-$intercepts. Recall that the $x-$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 $x=1$ and local minimums at $x=-2$ and $x=4.$

Note that this is only one of the infinitely many graphs with the given characteristics. Any graph with zeros at $-3,$ $1,$ and $5,$ a maximum at $x=1,$ and minimums at $x=-2$ and $x=4$ will be correct.