Graphing Polynomials and Multiplicity

• Positive Odd
• Positive Even
• Negative Odd
• Negative Even

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

• a
• b
• c
• d

• A
• B
• C
• D

In the above graph, which root has a multiplicity of 2?

• -1

• -3

• -120

• 4

What is the Factored Form for this graph? (Hint: does it have a multiplicity?)

• y= - (x+1)(x-2)(x-4)

• y= (x+1)²(x-3)(x-1)³

• y = 3x³ – 2x + 1

• y= (x+1)³(x-3)(x-1)²

Which roots have even multiplicity?

• -3

• 0

• 2

• Cannot be determined

Multiplicity.

Odd exponents: ____

Even Exponents: ____

• Odd - cross through x-axis

  Even - bounce

• Even - cross through x-axis

  Odd - bounce

• I really thought this was simple so I didn't care to take out my pencil and my spiral and write it down.

Which solution has a multiplicity of 2? 

• -1

• 1

• 3

• none of them do

• x=0 -crosses x

  x=2 -bounces

  x=3 -crosses x

• x=0 -bounces

  x=2 -crosses x

  x=3 -bounces

• ...Math bounces?