PPT-Sect. 2-3 Graphing Polynomial Functions

Objectives Identify Polynomial functions Determine end behavior recognize characteristics of polynomial functions Use factoring to find zeros of polynomial functions Polynomials of degree 2 or higher have graphs that are smooth and continuous By smooth we mean the graphs have rounded curves with no sharp corners By continuous we mean the graphs have no breaks and can be drawn without lifting your pencil from the rectangular coordinate system. Polynomials and Polynomial Functions. Definitions. Terms. Degree of terms and polynomials. Polynomial Functions. Evaluating. Graphing. Simplifying by Combining Like Terms. Adding & Subtracting Polynomials. 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.  . An order . differential equation has a . parameter family of solutions … or will it?.  . 0. 1. 2. 3. 4. 0. 0. 1. 2. 3. 4. 1. 1. 2. 3. 4. 0. 2. 2. 3. 4. 0. 1. 3. 3. 4. 0. 1. 2. 4. 4. 0. 1. 2. Algebra 2. Chapter 5. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Polynomial Function. Definition: A polynomial function of degree . n. in the variable x is a function defined by. Where each . a. i. (0 ≤ . i. ≤ n-1) is a real number, a. n. ≠ 0, and n is a whole number. . 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 . Quadratic Function. A . quadratic function . is defined by a quadratic or second-degree polynomial.. Standard Form. , . where . a. . ≠ 0. .. Vertex Form. , where a. . ≠ 0..  . Vertex and Axis of Symmetry. 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. 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. Standard 15. Graph and analyze polynomial and radical functions to determine:. Domain and range. X and y intercepts. Maximum and minimum values. Intervals of increasing and decreasing. End behavior. With the function: f(x) = . 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 .