PPT-Polynomial Functions

Algebra II with Trigonometry Ms Lee Essential Question What is a polynomial How do we describe its end behavior How do we addsubtract polynomials Essential Vocabulary Polynomial Degree. Mrs. . Chernowski. Pre-Calculus. Chris Murphy. Requirements:. At least 3 relative maxima and/or minima. The ride length must be at least 4 minutes. The coaster ride starts at 250 feet. The ride dives below the ground into a tunnel at least once. A). B). SYNTHETIC DIVISION:. STEP #1. : . Write the Polynomial in DESCENDING ORDER by degree and write any ZERO coefficients for missing degree terms in order. STEP #2. : . Solve the Binomial Divisor = Zero. Mustafa Mohamad. Department of Mechanical Engineering, MIT. 18.337, Fall 2016. Problem. Develop pure Julia codes for elementary function. Trigonometric functions. sin, cos, tan, . sincos. asin. , . acos. Boaz . Barak, . Nir. . Bitansky. , Ran Canetti,. Yael Tauman . Kalai, . Omer . Paneth, . Amit Sahai. Program Obfuscation . Obfuscated Program. Approved . Document . Signature . Obfuscation. Verify and sign. , . are.  . canonical.  solutions . y. (. x. ) of . Bessel's . differential equation. :. α (the . order.  of the Bessel function). Bessel functions are also known as . cylinder functions.  or . 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 . What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN. functions. Linear. y = 4x - 5. Cubic. y = 4x. 3. - 5. Fifth Power. y = 4x. 5. –x 5. Quadratics. 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) = . 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..