1 / 17

HA2 Ch. 5 Review

HA2 Ch. 5 Review. Polynomials And Polynomial Functions. Vocabulary. End behavior P.282 Monomial P.280 Multiplicity P. 291 Polynomial Function P.280 Relative Maximum/Min. P.291 Standard Form of a Poly. Function Synthetic Division P.306 Turning Point P. 282. 5-1 Polynomial Functions.

gertrudelee
Download Presentation

HA2 Ch. 5 Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. HA2 Ch. 5 Review Polynomials And Polynomial Functions

  2. Vocabulary • End behavior P.282 • Monomial P.280 • Multiplicity P. 291 • Polynomial Function P.280 • Relative Maximum/Min. P.291 • Standard Form of a Poly. Function • Synthetic Division P.306 • Turning Point P. 282

  3. 5-1 Polynomial Functions • Degree of a Polynomial – highest exponent • Standard Form – in descending order • Define a polynomial by degree and by number of terms – See green table on P. 281 • Maximum # of Turning points: n-1 • End behavior – the far left and far right of the graph

  4. Think in terms of a parabola If even, and a + Then end behavior upward facing End Behavior P. 282

  5. Think in terms of a parabola If even, and a negative Then end behavior downward facing End Behavior

  6. Think in terms of a parabola If ODD, and a + Then right end behavior upward facing, left is down End Behavior

  7. Think in terms of a parabola If ODD, and a negative Then right end behavior downward facing, left is up End Behavior

  8. Graphing Polynomial Functions • Step 1 – Find zeros and points in between. • Step 2 – “Sketch” graph • Step 3 – Use end behavior to check • Try to graph: y = 3x - x³ • Factored: 0 = x (3-x²) x = 0, ±√3

  9. Graph

  10. Assess • What is the end behavior and maximum amount of turning points in: (1.) y = -2x² - 3x + 3 (2.) y = x³ + x + 3

  11. (1.) down and down, max 1 turning point (2.) down and up, max two tp

  12. 5-2 Polynomials, Linear Factors, and Zeros • Factoring Polynomials: • GCF • Patterns: Diff of Squares, Perf. Sq. Trinomial • X-Method, Reverse Foil, Guess and Check • Set factors equal to zero and solve. • If those methods don’t work, then use Quadratic Formula to solve: • X =

  13. Multiplicity – Factor repeats • What are the zeros of f (x) = x⁴ - 2x³ - 8x² and what are their mult. ? • = x (x² - 2x – 8) • = x (x + 2)(x – 4) • x = 0 (x2), -2, and 4

  14. Writing a Function What is a cubic polynomial function in standard form with zeros 4, -1, and 2? y = (x – 4)(x + 1)(x – 2) y = (x² - 3x -4)(x – 2) y = x³ - 5x² + 2x + 8

  15. 5-3 Solving Polynomial Equations • Two more patterns for factoring: • Sum/Diff of Cubes: • a³ + b³ = (a + b)(a² - ab +b) • a³ – b³ = (a - b)(a² + ab +b) • Factor completely: x³ - 27 • = (x – 3)(x + 3x + 9) • What are the real/imaginary solutions? • Solve: x = 3, ±

  16. 5-3 Word Problem The width of a box is 2 m less than the length. The height is 1 m less than the length. The volume is 60 m³. What is the length of the box?

  17. 5-4 Dividing Polynomials Remember to write in standard form and put a zero place holder. Use long division to determine if (x – 2) is a factor of x - 32. Remember in synthetic division if you have a fraction to divide your answer by denominator.

More Related