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3.4 Notes - What is the maximum number of x-intercepts for...

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College Algebra Section 3.4 – Graphing Polynomial Functions First we are going to use our calculators to find the relative extrema (your text calls them “turning points”) and real zeros of a polynomial. Example: Graph 3 5 2 ) ( 2 3 - - - = x x x x f using your grapher and approximate each of the following to 3 decimal places. a. real zeros: _________________________ b. Relative Maximum: __________________ c. Relative Minimum: ________________ d. Interval(s) where f is increasing: _______________________ How many times can a 3 rd degree polynomial “turn”? _________ Could it have fewer turns? _____________ What is the maximum number of turns an n th degree polynomial can have? ___________________
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Unformatted text preview: What is the maximum number of x-intercepts for an n th degree polynomial? __________________ Now we will graph 3 4 2 ) 2 ( ) 1 ( ) ( +-= x x x x f by hand using the following steps: Steps for Graphing Polynomial Functions Factor Find x-intercepts and their multiplicities If the x-intercept has odd multiplicity, the graph crosses the x-axis at that point. If the x-intercept has even multiplicity, the graph is tangent to the x-axis at that point. Find the y-intercept Determine the behavior to the far left and far right by plugging in numbers to the left and right of all your x-intercepts....
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