Sketching Polynomials

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Sketching Polynomials

• by John Nguyen and Joyce Profil

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(No Transcript)
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Degree / Leading Coefficient

• Degree The degree of a polynomial is the highest
  exponent in the expression.
• Importance by looking at the degree, youll
  know that the line youll be graphing will have
  either the equal number of intercepts or fewer.
  If the degree is odd, opposite end behavior. If
  the degree is even, the direction of the end
  behavior is the same.
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• In the expression x5 2x4 2x3 4x2 2x 1,
  5 in x5, is the degree.
• In our graph, the degree is 5, so it will be
  going in opposite directions.
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• Leading Coefficient  The leading coefficient of
  a polynomial is the coefficient of the degree. It
  determines the direction of the whole graph. If
  it's positive, it's facing up.         
• If it's negative, it's facing down.
•  In the expression x5  2x4  2x3  4x2  2x 1,
  1 is the Leading Coefficient

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End Behavior

•  The appearance of a graph as it is followed
  farther and farther in either direction. For
  polynomials, the end behavior is indicated by
  drawing the positions of the arms of the graph,
  which may be pointed up or down. Other graphs may
  also have end behavior indicated in terms of the
  arms, or in terms of asymptotes or limits.
•  For an gt 0 and n even, f (x) infinity as x
  - infinity and f (x) infinity as x
  infinity
• For an gt 0 and n odd, f (x) - infinity as x -
  infinity and f (x) infinity as x infinity
• For an lt 0 and n even, f (x) - infinity as x
  - infinity and f (x) - infinity as x
  infinity
• For an lt 0 and n odd, f (x) infinity as x -
  infinity and f (x) - infinity as x infinity

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Local Maximum / Local Minimum

• Local Maximum Highest vertex of the equation.
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• Local Minimum Lowest vertex of the equation.

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Intercept form w/ multiplicities

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