Graph a Polynomial Function by hand
We graph a 3rd degree polynomial function by first gathering information about it. To find the y-intercept, we evaluate the function at zero (for our x-values). Then we factor it by using factor by grouping. When it is in factored form, we find our zeros (x-intercepts, roots) by thinking about what would need to replace x to make each factor equal zero. We then look at the exponent on each factor to find each zero's multiplicity. Based on whether each multiplicity is even or odd tells us if the function will touch or cross the x-axis. We locate the end behavior of the function by identifying the leading term and thinking about the end behavior of that power function. The last piece of information that we find is the maximum number of turning points by subtracting one from the degree of the polynomial. We finish by putting all of this information together for a nice graph of the polynomial function.
This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al. It is an open-source textbook from OpenStax that you may download for
free at https://openstax.org/details/books/al.... The text is licensed under the Creative Commons Attribution license. https://creativecommons.org/licenses/...
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