PPT-Analyze Graphs of Polynomial Functions

Objectives To approximate x intercepts of a polynomial function with a graphing utility To locate and use relative extrema of polynomial functions To sketch the graphs of polynomial functions. Neeraj. . Kayal. Microsoft Research. A dream. Conjecture #1:. The . determinantal. complexity of the permanent is . superpolynomial. Conjecture #2:. The arithmetic complexity of matrix multiplication is . Learning Goals:. Graphs of the Cosecant, Secant, and Cotangent Functions. Graph transformations . When you think about the . csc. , sec, and cot graphs what do you think about?. Graph of the Cosecant Function. Algebra II with . Trigonometry. Ms. Lee. Essential Question. What is a polynomial?. How do we describe its end behavior?. How do we add/subtract polynomials?. Essential Vocabulary. Polynomial . Degree. Dan Castillo. A Brief . H. istory of Knots. (1860’s). Lord Kelvin: . quantum vortices?. Let’s tabulate them just in case. First . table of knots by Peter . Tait. Aye aye!. Mathematical Study of Knots. Defn. : . Polynomial function. In the form of: . ..  . The coefficients are real numbers.. The exponents are non-negative integers.. The domain of the function is the set of all real numbers.. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . . A Reminiscence 1980-1988. Alexander Morgan. Part of the Prehistory of Applied Algebraic Geometry. A Series of (Fortunate) Unlikely Events. Intellectual epidemiology: . Idea originates with “case zero”. Section 4.5 beginning on page 190. Solving By Factoring. We already know how the zero product property allows us to solve quadratic equations, this property also allows us to solve factored polynomial equations [we learned how to factor polynomial expressions in the previous section].. Now, we have learned about several properties for polynomial functions. Finding y-intercepts. Finding x-intercepts (zeros). End behavior (leading coefficient, degree). Testing values for zeros/factors (synthetic division) . Section 2.4. Terms. Divisor: . Quotient: . Remainder:. Dividend: . PF. FF .  . Long Division. Use long division to find . divided by . ..  . Division Algorithm for Polynomials. Let . and . be polynomials with the degree of . Section 4.1. Polynomial Functions. Determine roots of polynomial equations. Apply the Fundamental Theorem of Algebra. Polynomial in one variable. A polynomial in one variable x, is an expression of the form a. Objective: . Recognize the shape of basic polynomial functions. Describe the graph of a polynomial function. Identify properties of general polynomial functions: Continuity, End Behaviour, Intercepts, Local . ••»••••• Online Polynomial Regression HomeContents LR LnR ExpR PowR PR MLR MPR NLR More...Contact This page allows performing polynomial regressions (polynomial l Algebra 2. Chapter 4. This Slideshow was developed to accompany the textbook. Big Ideas Algebra 2. By Larson, R., Boswell. 2022 K12 (National Geographic/Cengage). Some examples and diagrams are taken from the textbook..