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Polynomial Functions A polynomial function has to have exponents that are whole numbersThe following are NOT polynomials: 3 2 y 2x 4 x 5x 3 y 3 x x y 8
Degree and NameDegree – highest exponent of apolynomialConstantLinearQuadraticCubicQuarticQuintic
Homework Answers – p10610. a. r = ks b. 1.1; r = 1.1s c. about 45 mi/h11. b. F(v) = (60/9)v2 or F(v) = 6.67v2 c. 540 N14. No, there is an exponent that is a variable, not a constant16. a. d = 1, linear function or polynomial function of degree 1 b. f(6) = 2; f(0) = -7 c. -1018. d = 3; f(2) = -1
Direct Variation Functions A function that has no translation (shift) and has some symmetryExs. y = 2x y = -4x2 y = 3x3 y = -1/2x4
Factored Form 3 2y x 6x 11x 6y ( x 1)( x 2)( x 3)
Graphing from Factored FormFind the following:1. zeros (from the factors) and plot them2. y-intercept (let x = 0)3. degree to get the end behavior4. x-values in between zeros to get asketch of the graph
Graph y = 3x3 – 12xFirst, factor the polynomial.Show x and y intercepts!
MultiplicityA multiple zero is a repeated zero.Multiplicity is the number of times therelated linear factor is repeated in thefactored form of a polynomial.– use the exponent of the factor to determine it. 2 3 y ( x 2) ( x 2) ( x 5)
Standard form terms are written in descending order and all “like terms” are combined
Writing a polynomial in standard form.Example: y = (x – 1)(x + 2)(x – 4)What is the degree of the function?