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Powerpoint from Class on Polynomials

Powerpoint from Class on Polynomials

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  • 1. Height of RocketSeconds Feet 1 230 2 310 3 350 4 360 5 350 6 300 7 220
  • 2. Section 2.5 Polynomials andX and Y-intercepts
  • 3. 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
  • 4. Degree and NameDegree – highest exponent of apolynomialConstantLinearQuadraticCubicQuarticQuintic
  • 5. 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
  • 6. Direct Variation Functions A function that has no translation (shift) and has some symmetryExs. y = 2x y = -4x2 y = 3x3 y = -1/2x4
  • 7. Factored Form 3 2y x 6x 11x 6y ( x 1)( x 2)( x 3)
  • 8. 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
  • 9. Graph y = 3x3 – 12xFirst, factor the polynomial.Show x and y intercepts!
  • 10. 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)
  • 11. Standard form terms are written in descending order and all “like terms” are combined
  • 12. Writing a polynomial in standard form.Example: y = (x – 1)(x + 2)(x – 4)What is the degree of the function?
  • 13. Tonight’s HomeworkFinish 2.5 class worksheet
  • 14. Warmup – Graph each 2y x 6x 7y 2x 5 2 2y ( x 2) ( x 1)( x 4)
  • 15. Problem of the DaySimplify: 2 3/2 4 2 (9y ) ( 4y )
  • 16. Sketch the graph of: y = (x+2)(x-3)(x-3) Multiple root or Multiple zero Multiplicity = 2