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IM Alg2.2.10 Lesson: Multiplicity

Author:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

What do you notice? What do you wonder?




For polynomial A:

Write the degree, all zeros, and complete the sentence about the end behavior. Degree:                     Zeros:  End behavior: As x gets larger and larger in the negative direction,

Sketch a possible graph.

Check your sketch.

For polynomial B:

Write the degree, all zeros, and complete the sentence about the end behavior. Degree:                     Zeros:  End behavior: As x gets larger and larger in the negative direction,

Sketch a possible graph.

Check your sketch.

For polynomial C:

Write the degree, all zeros, and complete the sentence about the end behavior. Degree:                     Zeros:  End behavior: As x gets larger and larger in the negative direction,

Sketch a possible graph.

Check your sketch.

For polynomial D:

Write the degree, all zeros, and complete the sentence about the end behavior. Degree:                     Zeros:  End behavior: As x gets larger and larger in the negative direction,

Sketch a possible graph.

Check your sketch.

For polynomial E:

Write the degree, all zeros, and complete the sentence about the end behavior. Degree:                     Zeros:  End behavior: As x gets larger and larger in the negative direction,

Sketch a possible graph.

Check your sketch.

For polynomial F:

Write the degree, all zeros, and complete the sentence about the end behavior. Degree:                     Zeros:  End behavior: As x gets larger and larger in the negative direction,

Sketch a possible graph.

Check your sketch.

Pause here for your teacher to check your work. Create your own polynomial for your partner to figure out.

  • Create a polynomial with degree greater than 2 and less than 8 and write the equation in the space given.
  • Trade papers with a partner, then fill out the information about their polynomial and complete a sketch.
  • Trade papers back. Check your partner’s sketch using graphing technology.

Fill out this information about your partner's polynomial:

  • Degree:
  • Zeros:
  • End behavior: As gets larger and larger in the negative direction,

Sketch your partner's polynomial.

Check your partner's sketch.

Sketch a graph for a polynomial function  that has 3 different zeros and  for all values of .

What is a possible equation for the polynomial?

Use graphing technology to see if your equation matches your sketch.

What is a possible equation for the polynomial?

What is a possible equation of a polynomial function that has degree 5 but whose graph has exactly three horizontal intercepts and crosses the -axis at all three intercepts? Explain why it is not possible to have a polynomial function that has degree 4 with this property.

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