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$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

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Presentation on theme: "$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300."— Presentation transcript:

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9 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500

10 The graph of the equation is shown below.

11 What is y = (x + 1) 2 ?

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

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

15 What is

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

17 What is f(x) = (x – 3) 2 – 4?

18 The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 3x 2 – 18x Find the number of automobiles that must be produced to minimize the cost.

19 3 thousand automobiles

20 Determine if the following is a polynomial function. If so, give the degree. f(x) = x 2 – 3x 7

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24 Use the leading coefficient test to determine the end behavior for f(x) = 6x 3 + 3x 2 – 3x - 1

25 Up to the right, Down to the left.

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

27 -1, multiplicity 1 1, multiplicity 2

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

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30 Use synthetic division to divide. 3x x + 56 x + 7

31 3x + 8

32 Divide using synthetic division.

33 x 4 + 2x 3 + 5x x R. 45

34 Find f(-3) given f(x) = 4x 3 – 6x 2 – 5x + 6

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36 Solve the equation 3x 3 – 28x x – 14 = 0 given that 2 is one solution.

37 2, 7, 1/3

38 Use synthetic division to find all zeros of f(x) = x 3 – 3x 2 – 18x + 40.

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40 Use the rational zeros theorem to list all possible rational zeros of f(x) = x 5 – 3x 2 + 6x + 14

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

43 -1/3, 2, 4

44 Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and negative real zeros for f(x) = x 6 – 8.

45 1 positive real zero 1 negative real zero

46 Give all the roots of f(x) = x 3 + 5x x – 18

47 1, i, - 3 – 3i

48 Use the graphing calculator to determine the zeros of f(x) = x 3 – 6x 2 – x + 6 1, 3, 4, or 5

49 1, -1, 6

50 Use the Upper Bound Theorem to determine which of the following is a good upper bound for f(x) = x 4 + x 3 – 7x 2 – 5x , 3, 4, or 5

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52 Find all roots of the equation. Hint: -2i is one root. x 4 – 21x 2 – 100 = 0

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54 Write the polynomial function as a product of linear factors. f(x) = x 4 – 3x 2 – 4

55 f(x)= (x – 2)(x + 2)(x – i)(x + i)

56 Factor completely. f(x) = x 3 + 4x 2 – x - 4

57 f(x)= (x – 1)(x + 1)(x + 4)

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59 Give an equation for the polynomial function that has zeros of 2, -2, and 3 and has a degree of 3.

60 f(x)= (x – 2)(x + 2)(x – 3) Other answers are possible.

61 Solve the inequality and give your solution in interval notation. (x – 3)(x + 2) > 0

62 (-∞, -2) or (3, ∞)

63 Solve the inequality and give your solution in interval notation. x 2 + 3x – 18 > 0

64 (-∞, -6) or (3, ∞)

65 Solve the inequality and give your solution in interval notation. x 2 – 2x – 24 < 0

66 (-4, 6)

67 Solve the inequality and give your solution in interval notation. x 2 – 3x – 10 < 0

68 [-2, 5]

69 Solve the inequality and give your solution in interval notation. x 2 + 6x < – 8

70 [-4, -2]

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74 -10 < x < < y < 60

75 y = (x – 2) 2 (x + 3) 2


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