Modeling with Polynomial Functions - Lecture 3.9

Learn to model with higher degree polynomial functions in this comprehensive mathematics lecture and problem-solving session. Master writing equations for cubic functions using x-intercepts and additional points, working with factored form to solve for coefficients. Explore the relationships between constant differences in value tables, understanding how first-order differences indicate linear functions, second-order differences reveal quadratic functions, and higher-order differences correspond to cubic and quartic functions. Practice using calculators to model imperfect data and find curves of best fit for interpolation purposes, with special attention to cubic and quartic regressions. Work through 24 detailed practice problems with step-by-step solutions, including techniques for using graphing calculator features like regression equation copy-paste functionality. Note that while some mental calculations in problems 10 and 12 initially contain errors, they are corrected during the session, emphasizing the importance of calculator use for accuracy.