Warm Up: Solve

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Warm Up Solve Sketch the graph
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Graphing Polynomials Finding a Polynomial
Function
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Equivalent Statements

• x a is a zero of the function f.
• x a is a solution of the polynomial equation
  f(x)0.
• (x-a) is a factor of the polynomial f(x)
• (a, 0) is an x-intercept of the graph of f

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Multiplicity
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Repeated Zeros
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Sketch the graph
End behavior
Multiplicity of 2. Touches.
Through these Points.
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Multiplicity - repeated zero Means..

• If it occurs an odd number of times, the graph
  crosses the x-axis at the zero.
• If it occurs an even number of times, the graph
  will just touch the x-axis at the zero.

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Sketch the graph
1st Term would be
End Behavior
Mult. of 3 Goes Through
Mult. Of 2 Touches
x
y
1
3
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Sketch the graph
1st Term would be
End Behavior
Both have a multiplicity of 2. Just Touch!
x
y
-1
-1
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Can you write a polynomial function if you know
the zeros?
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Find a Polynomial function that has the given
zeros 6, -3
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Find a Polynomial function that has the given
zeros 0, 3, -5
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Find a Polynomial function that has the given
zeros 3, 2, -2, -1
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Find a Polynomial function that has the given
zeros and
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Long Synthetic Division
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Use Long Division and use the result to factor
the polynomial completely.
1st Step
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2nd Step
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Divide using long division
Remainder
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Divide using long division
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You Try Divide using long division
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Divide using long division
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Synthetic Division
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(No Transcript)
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Divide using synthetic division to find the zeros
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Divide using synthetic division
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You Try Divide using synthetic division Find
zeros
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You Try Divide using synthetic division
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You Try Divide using synthetic division