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Algebra II Task: Fourth Degree Polynomial

Algebra II Task: Fourth Degree Polynomial

PDF icon Algebra II Task: Fourth Degree Polynomial

Standards & Objectives

Essential and guiding questions: 
  • What helped you come up with the polynomial without the x3 or x term?
  • Would all the polynomials that would fit these criteria have the same general shape?
  • What do you notice about all of the terms in the polynomials groups came up with?
  • What do you notice about the symmetry of this graph?
  • Can we determine the ordered pairs of the absolute minimums?
  • Can we determine the ordered pair of the relative maximum?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….

Assessing

  • How did you come up with the second degree polynomial in the pre problem work?

Advancing

  • How can we use this information to help us in creating the fourth degree polynomial?
Extension suggestions: 

If students finish early….
Assessing 

  • What if the leading coefficient of your polynomial was 2. What effect(s) would that have on your graph?

Advancing 

  • Can you find the ordered pairs of the lowest points on the graph?
Originator: 
Tennessee Department of Education