# Multiplicity of zeros of functions student activity sheets

This Multiplicity of Zeros of Functions Lesson Plan is suitable for 9th - 12th Grade. Pupils identify the multiplicity of exponents as they graph polynomials. They write equations for a function given the zeros of the function and work backwards from solving equations. ©y w2h0z1 C2Q OKdu ytha c lSBoGfit 6w 3a krQeF xLRL ECm.D S XAblQlb jr Uivg 6hYtcst ZrOeHs ge 1rXvXejd g.e h NMmabd fej nw5iitbhG fItn zfTinaiOtle c PAulSgze Ib TreaG Y2B.V Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Factors and Zeros Date_____ Period____ Find all zeros. 1) 2.3 Polynomial Functions of Higher Degree with Modeling PreCalculus 2 - 7 Example 5: State the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding -xintercept. Using what you know about end behavior and the zeros ofthe

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Finding the Zeros of a Polynomial Function A couple of examples on finding the zeros of a polynomial function. Example: Find all the zeros or roots of the given functions. f(x) = 3x 3 - 19x 2 + 33x - 9 f(x) = x 3 - 2x 2 - 11x + 52. Show Step-by-step Solutions In my discovery activity, my aim is for students to discover the pattern for determining the end behavior of higher degree polynomial functions. In the notes afterwards, my aim is to solidify this knowledge and to teach students how to sketch the graphs of these polynomials by finding their zeros.

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All four graphs have the same zeroes, at x = –6 and at x = 7, but the multiplicity of the zero determines whether the graph crosses the x -axis at that zero or if it instead turns back the way it came. coefficient. The graph will at the zero of x = , at the zero of x = , and at the zero of x = . 6. A polynomial with a real zero with multiplicity four and two imaginary zeros must be a degree polynomial. Write a factored form polynomial function f(x) of least degree that has a leading coefficient of 1 with the real zeros shown in the graph. 7. Polynomial Functions (Review) Functions: Zeros / X-Intercepts / Solutions / Factors - Notes Repeated Zeros of a Polynomial, 3 Cases - Notes Factoring Polynomials: Zeros and Multiplicity Summary - Notes Factoring a Polynomial by Using Its Graph 1 - Worksheet, Key

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This lesson merges graphical and algebraic representations of a polynomial function and its linear factors. As a result, students will: Manipulate the parameters of the linear functions and observe the resulting changes in the polynomial function. Find the zeros of the polynomial equations by finding the zeros of the linear factors.

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I plan to begin by having students complete page 2 of Multiplicity of Zeros Day 1 (p.1-2). If students do not recall zeros of a function, you can remind them. Here is a straight forward hint: find the values for x that make f (x) = 0. Push the students to come up with an algebraic solution,... Here is a set of practice problems to accompany the Zeroes/Roots of Polynomials section of the Polynomial Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University.

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6.1-6.6 Review Worksheet Page 2 of 5 Write a polynomial having the given zeros, first in factored form, then multiply it out and put it in standard form. When a factor is repeated in a function, this results in a zero." In other words: the zero has multiplicity of n, where n is the number of times that zero appears as a factor. Key Concept How Multiple Zeros Affect a Graph If a is a zero of multiplicity n in the polynomial function y = P(x), then the behavior of

MAT140 Section 5.1 Worksheet on Polynomial Functions Part I. Create a polynomial with lead coe cient 1 having the following characteristics: 1. Zeros at x = 1 and x = 1; and having degree 2 2. Zeros at x = 1 and x = 0; and having degree 3 3. Zeros at x = 0, x = 1, x = 2 3, and x = 3; and having degree 4 4. coefficient. The graph will at the zero of x = , at the zero of x = , and at the zero of x = . 6. A polynomial with a real zero with multiplicity four and two imaginary zeros must be a degree polynomial. Write a factored form polynomial function f(x) of least degree that has a leading coefficient of 1 with the real zeros shown in the graph. 7. This lesson merges graphical and algebraic representations of a polynomial function and its linear factors. As a result, students will: Manipulate the parameters of the linear functions and observe the resulting changes in the polynomial function. Find the zeros of the polynomial equations by finding the zeros of the linear factors. When a factor is repeated in a function, this results in a zero." In other words: the zero has multiplicity of n, where n is the number of times that zero appears as a factor. Key Concept How Multiple Zeros Affect a Graph If a is a zero of multiplicity n in the polynomial function y = P(x), then the behavior of

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Algebra II Notes Polynomial Functions Unit 4.6 – 4.7 Alg II Notes Unit 4.6-4.7 Graphing Polynomial Functions Page 7 of 16 9/12/2014 Ex 3: Indicate if the degree of the polynomial function shown in the graph is odd or even and indicate the sign of the If the remainder is zero, then it IS a FACTOR Fundamental Theorem of Algebra The degree of a polynomial is equal to the number of roots/zeros of the polynomial (counting multiplicity). 2.3 Polynomial Functions of Higher Degree with Modeling PreCalculus 2 - 7 Example 5: State the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding -xintercept. Using what you know about end behavior and the zeros ofthe We say that x = h is a zero of multiplicity p. The graph of a polynomial function will touch the x -axis at zeros with even multiplicities. The graph will cross the x -axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function. Jul 16, 2015 · 🔴 Deep Sleep Music 24/7, Sleep Therapy, Relax, Insomnia, Meditation, Calm Music, Spa, Study, Sleep Yellow Brick Cinema - Relaxing Music 7,465 watching Live now zeros of polynomial functions task cards plus guided notes precalculus, pre calc worksheet real zeros of polynomials elegant power functions, advanced pre calculus advanced pre calculus, advanced pre calculus advanced pre calculus and chapter 2 ms kildea. Of chapter 2 ms kildea, pre calc worksheet real zeros of polynomials elegant power functions.

Graphs of Polynomial Functions Name_____ Date_____ Period____-1-For each function: (1) determine the real zeros and state the multiplicity of any repeated zeros, (2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph.

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This lesson merges graphical and algebraic representations of a polynomial function and its linear factors. As a result, students will: Manipulate the parameters of the linear functions and observe the resulting changes in the polynomial function. Find the zeros of the polynomial equations by finding the zeros of the linear factors. Learn about the relationship between the zeros, roots, and x-intercepts of polynomials. Learn about zeros multiplicities. ©y w2h0z1 C2Q OKdu ytha c lSBoGfit 6w 3a krQeF xLRL ECm.D S XAblQlb jr Uivg 6hYtcst ZrOeHs ge 1rXvXejd g.e h NMmabd fej nw5iitbhG fItn zfTinaiOtle c PAulSgze Ib TreaG Y2B.V Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Factors and Zeros Date_____ Period____ Find all zeros. 1) Graphs of Polynomial Functions Name_____ Date_____ Period____-1-For each function: (1) determine the real zeros and state the multiplicity of any repeated zeros, (2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph. Sep 26, 2016 · This algebra 2 and precalculus video tutorial explains how to graph polynomial functions by finding x intercepts or finding zeros and plotting it using end behavior and multiplicity. This video ... Directions: Find the zeros of each polynomial and state the multiplicity of any multiple zeros. a) yxx x 33 b) f (x) x4 6x3 8x2 c) f (x) (x 2)(x 1)(x 1)2 d) xx x32 44 Sometimes you might know the zeros of a function, but need to find the equation in standard form. (Review: why do we need an equation in standard form sometimes?) We’ve already determined the zeroes of each of these in previous work or examples in this section so we won’t redo that work. In each case we will simply write down the previously found zeroes and then go back to the factored form of the polynomial, look at the exponent on each term and give the multiplicity.

Identify the graph of the polynomial function f. f(x) = x 4 + x 3 - 2x 2 Click here to see the graphs. More References and Links to Tutrials on Polynomial Functions Polynomial Functions Multiplicity of Zeros and Graphs Polynomials Polynomial Functions, Zeros, Factors and Intercepts Find Zeros of Polynomial Functions - Problems 2.3 Polynomial Functions of Higher Degree with Modeling PreCalculus 2 - 7 Example 5: State the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding -xintercept. Using what you know about end behavior and the zeros ofthe