Polynomials
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The document discusses key aspects of polynomials including degree, end behavior, and graph shapes. The degree of a polynomial determines the general shape of its graph and the maximum number of x-intercepts. The end behavior describes what the polynomial function does as it approaches positive and negative infinity, which depends on the sign of the leading term. Polynomials with an even degree and positive leading term have graphs that start and end at positive infinity, while those with an even degree and negative leading term have graphs that start at positive infinity and end at negative infinity.
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3. X-intercepts and y-intercepts are found by setting the polynomial equal to 0 or the variable equal to 0.
4. The multiplicity of intercepts determines whether the graph crosses or touches the x-axis at that point.Graphing Polynomials
Graphing PolynomialsLogan_K_Jones
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This document provides steps for graphing polynomials: 1) Identify the polynomial function; 2) Find the degree by adding exponents; 3) Determine if the graph starts and ends at the top or bottom based on degree and signs; 4) Find x-intercepts by switching signs in the function; 5) Determine if the line passes through, bounces off, or squiggles at intercepts based on exponents; 6) Graph the polynomial using the above steps.Polynomia ls 
Polynomia ls leemad10
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This document defines and provides examples of polynomials. A polynomial is a function with real number coefficients and whole number exponents. To analyze a polynomial, you find its zeros, degree, and left and right end behavior, then graph it. The degree determines the direction of the graph's arrows. Even degrees have up arrows, odd degrees have one up and one down, and negative degrees reverse the arrows. The document also defines degree as the sum of exponents and root behavior as how a line passes through zeros. An example polynomial is worked through to demonstrate.5.1[1]![5.1[1]](https://cdn.slidesharecdn.com/ss_thumbnails/5-11-121219075353-phpapp01-thumbnail.jpg?width=560&fit=bounds)
5.1[1]leblance
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This document defines key concepts related to polynomials and polynomial functions. It defines monomials as terms involving variables and exponents, and polynomials as sums of monomials. The degree of a polynomial is the highest exponent among its terms. Polynomial functions are polynomials written in terms of a single variable. Standard form arranges polynomial terms by descending degree. Polynomials are classified by degree and number of terms. Higher degree polynomials can have more turning points and their end behavior depends on the leading term. Examples show determining standard form, classifying polynomials, identifying end behavior and increasing/decreasing parts of graphs.5.1 part 1
5.1 part 1leblance
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This document summarizes key concepts about polynomial functions including:
- Definitions of monomials, polynomials, and polynomial functions
- The standard form and classification of polynomials by degree and number of terms
- How the degree of a polynomial affects the shape of its graph, including the number of turning points and end behavior
- Examples of determining the end behavior and classifying increasing and decreasing parts of polynomial graphs10 b krishna
10 b krishnaKrishna Gupta
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The document defines key terms related to polynomials including: monomial, polynomial, binomial, trinomial, degree of a monomial/polynomial, and standard form. It provides examples of classifying polynomials by degree and number of terms. The document also discusses writing polynomials in standard and factored form, finding the leading coefficient, and relating the zeros of a polynomial to its x-intercepts. Examples are worked through of writing polynomials in standard form and classifying them by degree and number of terms.Power point presentationCORRELATION.pptx
Power point presentationCORRELATION.pptxSimran Kaur
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This document discusses different types of correlation and methods for determining correlation between variables. It defines correlation as the relationship between two or more variables, and describes positive correlation as variables changing in the same direction and negative correlation as changing in opposite directions. It also distinguishes between simple correlation of two variables and multiple correlation of more than two variables. Additionally, it introduces several methods for measuring correlation, including scatter plots, Karl Pearson's coefficient of correlation, and Spearman's rank correlation coefficient.
Graphing polynomials
Graphing polynomialsmakenziew1
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The document discusses how to graph polynomials by determining the x-intercepts from the zeros of the polynomial, the y-intercept, and the behavior at infinity using the leading coefficient test. It provides details on how the multiplicity of zeros relates to whether x-intercepts cross or touch the x-axis, and whether the graph is flat at those points. An example graphing the polynomial f(x)=x^5-5x^4+10x^3-10x^2+5x-40 is worked through step-by-step.Polynomial PowerPoint Presentation for CBSE
Polynomial PowerPoint Presentation for CBSEprimepaathshala
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The students of class 8th-10th of CBSE/ICSE and other state boards can learn the concept of polynomial from this latest uploaded PowerPoint Presentation. This presentation has covered all the key concept and definition of Polynomial chapter of Math's. This presentation is also beneficial for teachers who want to teach Polynomial concept to their students. The slides have been designed to be used in smart screen for teaching. 6.3 evaluating-and-graphing-polynomila-functions
6.3 evaluating-and-graphing-polynomila-functionsmorrobea
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This document discusses polynomial functions. It defines polynomial functions as functions of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where the exponents are whole numbers. It describes the leading coefficient, constant term, and degree of a polynomial function. Common types of polynomial functions like constant, linear, quadratic, cubic, and quartic functions are identified based on their degree. Methods for identifying if a function is a polynomial function, evaluating polynomial functions using direct substitution and synthetic substitution, and determining the left and right behavior of a polynomial function's graph are also discussed.6.3 evaluating-and-graphing-polynomila-functions
6.3 evaluating-and-graphing-polynomila-functionsmorrobea
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This document discusses polynomial functions. It defines polynomial functions as functions of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where the exponents are whole numbers. It describes the leading coefficient, constant term, and degree of a polynomial function. Common types of polynomial functions like constant, linear, quadratic, cubic, and quartic functions are summarized. Methods for identifying if a function is a polynomial function, evaluating polynomial functions using direct substitution and synthetic substitution, and determining the left and right behavior of a polynomial function's graph are also discussed.Module 2 Lesson 2 Notes
Module 2 Lesson 2 Notestoni dimella
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This document defines polynomial functions and discusses their key properties. It defines polynomials as expressions with real number coefficients and positive integer exponents. Examples of polynomials and non-polynomials are provided. The document discusses defining polynomials by degree or number of terms, and classifying specific polynomials. It covers finding zeros of polynomial functions and their multiplicities. The document also addresses end behavior of polynomials based on the leading coefficient and degree. It provides an example of analyzing a polynomial function by defining it, finding zeros and multiplicities, describing end behavior, and sketching its graph.Intro to Polynomials
Intro to Polynomialscmorgancavo
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This document discusses polynomials and their graphs. It defines a polynomial as an expression with two or more algebraic terms separated by plus and minus signs. Polynomials are named based on their degree and number of terms, with the degree being the highest exponent of its terms. The general shapes of polynomial graphs are constant for linear polynomials, parabolic for quadratics, cubic for cubics, and so on. Important features of polynomial graphs discussed include x-intercepts, y-intercepts, regions of increase/decrease, relative maxima/minima, and end behavior determined by degree and leading coefficient.Polynomials
- 1. Polynomials Taylor L Payne
- 2. First you determine the degree by the end behavior, or the exponents. And decide wether its an odd or even number. For example in the problem above there are exponents 2, 1, and 3 so the degree is 6. Which is an even number.The degree of the polynomial is absolutely key to graphing it. The degree tells a good amount of information about the graph. The first thing it tells us is the general shape of the polynomial, such as does it start from the bottom and continue to the top, or does it start at the top and curve its way back to the top? The second thing it tells us is the number of possible x-intercepts the graph might have.The end behavior of a polynomial function is a description of how the polynomial behaves as it approaches positive and negative infinity. In other words, what does the polynomial do at the two ends of the graph? Some go up to infinity on one side and down to negative infinity on the other. Some have each end go to positive infinity. The end behavior is totally dependent on the leading term of the polynomial function when simplified
- 3. Positives This shape results if the leading term is positive and the degree of the polynomial is even. An example would be y = 2x2+4x-3. The degree of the equation is 2 (even), and its leading coefficient, 2x2, is positive.
- 4. Negatives This shape results if the leading term is negative and the degree of the polynomial is even. An example would be y = -2x4+3x3+x-7. The degree of the equation is 4 (even), and its leading coefficient, -2x4, is negative.