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How does the multiplicity of a zero determine the behavior of the graph at that zero?

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A seventh degree polynomial function has zeros of −6 (multiplicity of 2), 0, 1 (multiplicity of 3), and 4.

Please, I really don't understand this question

 Jan 7, 2024
 #1
avatar+129690 
+1

A  zero with an even multiplicity will touch (but not go  through) the x axis     -  behavior 1

 

A zero with a multiplicity of 1 will  go through the x axis   - behavior 2

 

A  zero  with an odd multiplcity  >  1 will  "flatten out" a bit before crossing the  x axis  - behavior 3

 

 

 

 

zero                      multiplicity                       behavior

-6                              2                                      1

 0                              1                                       2

 1                              3                                       3

  4                             1                                       2                 

 

 

Corrected!!!

 

 

cool cool cool

 Jan 7, 2024
edited by CPhill  Jan 7, 2024
 #2
avatar+15 
+1

Thank you sooo much CPhill, like really you are amazing :D

wilmaaaa  Jan 7, 2024

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