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Mastering Polynomial Functions: Graphing and Analysis

Understand how to graph polynomial functions symbolically and identify key graph features. Classify polynomials by degree and number of terms, analyze end behavior, turning points, and relative extrema. Practice graphing and analyzing polynomial functions.

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Mastering Polynomial Functions: Graphing and Analysis

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  1. 5.1Polynomial Functions • Learning goals • graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. • graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. 

  2. monomial : a number, a variable, or the product of a real number and variables with whole number exponents polynomial : a monomial or the sum of monomials degree : • For a monomial – the sum of its exponents • For a polynomial – the largest sum of exponents from a term **Always put answers in standardform: descending order of exponents Vocabulary

  3. By Degree • 0 – constant • 1 – linear • 2 – quadratic • 3 – cubic • 4 – quartic • 5 – quintic By # of Terms • 1 – monomial • 2 – binomial • 3 – trinomial • 4 or more - polynomial ClassifyingPolynomials Shape

  4. Put in standard form • What is the degree of the polynomial? • Classify each polynomial by degree and number of terms • What shape is it? Ex 1

  5. Write in standard form, classify, state degree and shape. Ex 2

  6. The degree of a polynomial function affects • the shape of its graph • the maximum number of turning points • the way behaves at its ends turning point : places where a graph changes direction end behavior : direction of the graph where the arrows appear (far left and far right of the graph) Vocabulary

  7. relative minimum /relative maximumpeaks and valleys within the graph of a polynomial that has several turning points Vocabulary

  8. Find the relative minimum and maximum Ex 3

  9. End Behavior

  10. Ex 4 • Describe the end behavior • Is the graph odd or even? • Is the leading coefficient positive or negative? • Relative max or min?

  11. Ex 5 • Describe the end behavior • Is the graph odd or even? • Is the leading coefficient positive or negative? • Relative max or min?

  12. Ex 6 For each polynomial function: • describe the end behavior • sketch

  13. Ex 7 For each polynomial function: • describe the end behavior • sketch

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