Pc 2.2 a_notes

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Introduction to polynomials, leading coefficients test, and zeros.

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Pc 2.2 a_notes

  1. 1. 2.2 PolynomialFunctions of HigherDegreeEssential Question:What is the leading coefficient test? 1
  2. 2. Graphs of Polynomial FunctionsCharacteristics of a polynomial graph:- __________ (no breaks, holes, or gaps)- __________ (no sharp edges) 2
  3. 3. Whats a Power Function? Even Odd 3
  4. 4. Whiteboards! 4
  5. 5. Transformations!Ex. 1) Graph. 5
  6. 6. Leading Coefficient TestAs x moves without bound __________ or__________, the graph of the polynomialfunction eventually ___________ or__________ in the following manner:n is _____: 6
  7. 7. n is ______:What does this mean? 7
  8. 8. Rally Coach:Describe the left and right hand behavior of thefunction. 8
  9. 9. Zeros of a Polynomial FunctionGiven f is a function of degree n: Number of real zeros: Number of turning points: 9
  10. 10. Real Zeros of Polynomial Functions If f is a polynomial function and a is a real number, the following statements are equivalent: 1) ________ is a _________ of the function f. 2) ________ is a _________ of the polynomial equation f(x) = 0. 3) ________ is a _________ of f(x). 4) ________ is an _____________ of the graph of f. 10
  11. 11. *** Add this below the Real Zeros Slide!Repeated ZerosA factor (x-a)k yields a repeated zero x = aof ___________ k.1) If k is ______, the graph _________x-axis at x = a.2) If k is ______, the graph _________the x-axis at x = a 11
  12. 12. Ex. 2) Find all real zeros ofDetermine the number of turning points as well. 12
  13. 13. Bonus Example!!Ex. 3﴿ Find a 5th degree polynomial with x=­3, 1, 5, and 6 as zeros. 13
  14. 14. Assignment:2.2A p. 148 #13-21(odd), 27-41 (odd) 14

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