1 / 74

Quadratic Functions

Learn about quadratic functions, polynomial graphs, synthetic division, zeros, and inequalities. Dive deep into polynomial roots, cost optimization, and rational zeros. Boost your understanding and mastery of these mathematical concepts.

kimberlyhines
Download Presentation

Quadratic Functions

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. Quadratic Functions

  2. Polynomial Functions & Graphs

  3. Synthetic Divison

  4. Zeros of Polynomial Functions

  5. More on Zeros of Polynomials

  6. Solving Inequalities

  7. Quadratic Functions Polynomial Functions & Graphs Synthetic Division Zeros of Polynomial Functions More on Polynomial Zeros Solving Inequalities $100 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 $500

  8. The graph of the equation is shown below.

  9. What is y = (x + 1)2?

  10. The equation of the parabola with this vertex is f(x) = (x + 8)2 - 4

  11. (-8, 4)

  12. The function for this graph is f(x) = (x – 5)2 – 1.

  13. What is

  14. This quadratic equation has a maximum point at (3, -4).

  15. What is f(x) = (x – 3)2 – 4?

  16. The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 3x2 – 18x + 63. Find the number of automobiles that must be produced to minimize the cost.

  17. 3 thousand automobiles

  18. Determine if the following is a polynomial function. If so, give the degree. f(x) = x2 – 3x7

  19. Yes. Degree = 7

  20. Does the graph represent a polynomial function?

  21. Yes

  22. Use the leading coefficient test to determine the end behavior for f(x) = 6x3 + 3x2 – 3x - 1

  23. Up to the right, Down to the left.

  24. Find the zeros and their multiplicities of the function. F(x) = 4(x + 5)(x – 1)2

  25. -1, multiplicity 1 1, multiplicity 2

  26. Graph the function. F(x) = x2(x – 3)(x – 2)

  27. Use synthetic division to divide. 3x2 + 29x + 56 x + 7

  28. 3x + 8

  29. Divide using synthetic division.

  30. x4 + 2x3 + 5x2 + 10x + 20. R. 45

  31. Find f(-3) given f(x) = 4x3 – 6x2 – 5x + 6

  32. -141

  33. Solve the equation 3x3 – 28x2 + 51x – 14 = 0 given that 2 is one solution.

  34. 2, 7, 1/3

  35. Use synthetic division to find all zeros of f(x) = x3 – 3x2 – 18x + 40.

  36. 2, 5, -4

  37. Use the rational zeros theorem to list all possible rational zeros of f(x) = x5 – 3x2 + 6x + 14

  38. Use the rational zeros theorem to list all possible rational zeros of f(x) = 3x3 – 17x2 + 18x + 8 and then use this root to find all zeros of the function.

  39. -1/3, 2, 4

  40. Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and negative real zeros for f(x) = x6 – 8.

  41. 1 positive real zero 1 negative real zero

  42. Give all the roots of f(x) = x3 + 5x2 + 12x – 18

  43. 1, -3 + 3i, - 3 – 3i

  44. Use the graphing calculator to determine the zeros of f(x) = x3 – 6x2 – x + 6 1, 3, 4, or 5

  45. 1, -1, 6

  46. Use the Upper Bound Theorem to determine which of the following is a good upper bound for f(x) = x4 + x3 – 7x2 – 5x + 10 1, 3, 4, or 5

  47. 3

More Related