Pc 2.2 a_notes
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2.2 Polynomial Functions of Higher DegreeEssential Question:What is the leading coefficient test?
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Graphs of Polynomial FunctionsCharacteristics of a polynomial graph:
- __________ (no breaks, holes, or gaps)
- __________ (no sharp edges)
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What's a Power Function?
Even Odd
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Whiteboards!
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Transformations!Ex. 1) Graph.
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Leading Coefficient TestAs x moves without bound __________ or __________, the graph of the polynomial function eventually ___________ or __________ in the following manner:
n is _____:
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n is ______:
What does this mean?
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Rally Coach:
Describe the left and right hand behavior of the function.
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Zeros of a Polynomial Function
Number of real zeros:
Number of turning points:
Given f is a function of degree n:
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Real Zeros of Polynomial FunctionsIf 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.
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*** Add this below the Real Zeros Slide!
Repeated ZerosA factor (x-a)k yields a repeated zero x = a of ___________ k.
1) If k is ______, the graph _________ x-axis at x = a.
2) If k is ______, the graph _________ the x-axis at x = a
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Ex. 2) Find all real zeros of Determine the number of turning points as well.
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Ex. 3﴿ Find a 5th degree polynomial with x=3, 1, 5, and 6 as zeros.
Bonus Example!!
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Assignment:
2.2A p. 148 #13-21 (odd), 27-41 (odd)