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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