polynomial review
DESCRIPTION
Polynomial Review. OBJ: SWBAT analyze and graph polynomials. Definition. Definition: A polynomial function is a function where…. Terms:. Analyzing Standard Form. F(x) = Key Info: Degree: Leading Coefficient: Y-intercept: # roots: # extrema:. Analyzing Standard Form Con’t.d. - PowerPoint PPT PresentationTRANSCRIPT
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Polynomial Review
OBJ: SWBAT analyze and graph polynomials
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Definition
Definition: A polynomial function is a function where….
Terms:
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Analyzing Standard Form
F(x) = Key Info:Degree:Leading Coefficient:Y-intercept:# roots:# extrema:
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Analyzing Standard Form Con’t.d
End Behavior
Positive Negative
Even
Odd
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Example
f(x) = 7x5 – 2x2 + 9Deg: ____LC: ____Y-int: ____E.B.: ____# roots: ____# extrema: ____
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Factored Form
F(x) = a(x – f1)n(x – f2)n…..
Where….
Degree:LC:Y-int:**
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Example:
f(x) = -2(x – 3)2(x + 4)4(2x – 1)2
Deg: ____LC: ____Y-int: ____E.B.: ____# roots: ____# extrema: ____Roots: ____
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X-intercepts
X-intercepts = roots = zeroes If k is a root, then f(k) = 0 or (x – k) is
a factor How to determine:
Synthetic or Long Division
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Synthetic Division Example
Divide 3x3 – 2x2 + 6 by x + 1
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Tips to Finding Roots
1) Descartes Theorem:
2) Rational Roots Theorem
3) Use division to verify
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Example
f(x) = x3 – x2 – 25x + 25
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Steps to Graphing
1)2)3)4)5)
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Example
f(x) = x4 – x3 – 21x2 + x + 20