PPT-3.5 Higher – Degree Polynomial Functions and Graphs

Polynomial Function Definition A polynomial function of degree n in the variable x is a function defined by Where each a i 0 i n1 is a real number a n 0 and n is a whole number . Classify polynomials and write polynomials in standard form. . Evaluate . polynomial expressions. .. Add and subtract polynomials. . Objectives. monomial. degree of a monomial. polynomial. degree of a polynomial. The vertical scale is too big or too small, or skips numbers, or doesn’t start at zero.. The graph isn’t labeled properly.. Data is left out.. But some real life misleading graphs go above and beyond the classic types. Some are intended to mislead, others are intended to shock. And in some cases, well-meaning individuals just got it all plain wrong. These are some of my favorite recent-history misleading graphs from real life.. Polynomials. Monomials in one variable. The product of a constant and a variable raised to a nonnegative integer power.. 2x. 4. 2 is the coefficient degree is 4. What does it mean to be raised to a nonnegative integer power?. 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.. 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. . 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”. The degree of a polynomial is calculated by finding the . largest exponent. in the polynomial. .. Degree of a Polynomial. (Each degree has a special “name”). 9. Degree of a Polynomial. (Each degree has a special “name”). 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 . 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) = . Professional Programs at SUNY. SUNY Professional Programs. Architecture. Dentistry. Law. Medicine & Osteopathic . Nurse Practitioner . Occupational Therapy . Optometry. . Pharmacy. Physical Therapy . transformations of these graphs. LO: SWBAT state the transformations of the sine and cosine. Graphs in words.. CO: SWBAT generate the graphs of the sine and cosine functions and explore various . transformations of these graphs. LO: SWBAT state the transformations of the sine and cosine. 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..