We graph a factored polynomial function by first gathering information about it. To find the y-intercept, we evaluate the function at zero (for our x-values). To find our zeros (x-intercepts, roots) we think 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. 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 [ Ссылка ]. The text is licensed under the Creative Commons Attribution license. [ Ссылка ]
