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Polynomial Functions

Polynomial Functions. Polynomial Functions. A polynomial is a monomial or the sum of monomials. A Polynomial Function: P(x) = a n x n + a n-1 x n-1 + … + a 1 x + a 0 Where n is a nonnegative integer and the coefficients a n …a 0 are real numbers. Standard Form of a Polynomial.

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Polynomial Functions

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  1. Polynomial Functions

  2. Polynomial Functions A polynomial is a monomial or the sum of monomials. A Polynomial Function: P(x) = anxn + an-1xn-1 + … + a1x + a0 Where n is a nonnegative integer and the coefficients an…a0 are real numbers

  3. Standard Form of a Polynomial The DEGREE of a term is determined by the exponent of the variable. STANDARD FORM is when the terms are ordered in DECENDING order by degree. P(x) = 2x3 – 5x2 – 2x + 5

  4. Writing in Standard Form http://www.youtube.com/watch?v=hsAdZaHv3ZA 3x2 + 4x5 – 3x3 + 5x2

  5. Classifying Polynomials We can classify polynomials in two ways: • By the number of terms

  6. Classifying Polynomials We can classify polynomials in two ways: • By the degree of the polynomial (or the largestexponent of any term of the polynomial).

  7. Classifying Polynomials Classify it by degree AND number of terms. http://www.youtube.com/watch?v=XeScfpyMMk8 • 7x + 42. 3x2 + 2x +1 3.4x3 4. 9x4 + 11x 5. 5

  8. Graphs of Polynomials Linear Cubic Quadratic Quartic Quintic

  9. Cubic Regression We have already discussed regression for linear functions, and quadratic functions. We can also determine the Cubic model for a given set of points using Cubic Regression. STAT  Edit x-values in L1, y-values in L2 STAT CALC 6:CubicReg

  10. Cubic Regression http://www.youtube.com/watch?v=DTwoiqhfmxY Find the cubic model for each function, find y when x = 17. • (1,91), (10,95), (20,260), (30,365) • (10, 0), (11,121), (12, 288), (13,507)

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