Solving Non-Linear Equations - Edl Web viewIf false, replace the underlined word or words to make a true sentence. 4. is an example of a quadratic equation. 5. In , the constant term

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Solving Non-Linear Equations

Indicate whether the statement is true or false. If it is false, change the identified word(s) to make the statement true.

Write whether each sentence is true or false. If false, replace the underlined word or words to make a true sentence.

4. is an example of a quadratic equation.

5. In , the constant term is .

Write whether each sentence is true or false. If false, replace the underlined word or words to make a true sentence.

6. In , theleading coefficient is 3x2.

Indicate the answer choice that best completes the statement or answers the question.

Solve each inequality.

7. 9x2 + 36x + 36 0A. all real numbersB. {x | x = –2}C. {x | x< –2}D. {x | x –2}

Determine whether each function has a maximum or minimum value, and find that value. Then state the domain and range of the function.

8. f(x) = 2x2 + 4x – 6A. minimum; –1; all real numbers; {f(x) | f(x) –1}B. minimum; –6; all real numbers; {f(x) | f(x) –6}C. maximum; –8; all real numbers; {f(x) | f(x) –8}D. minimum; –8; all real numbers; {f(x) | f(x) –8}


9. FENCING Vanessa has 180 feet of fencing that she intends to use to build a rectangular play area for her dog. She wants the play area to enclose at least 1800 square feet. What are the possible widths of the play area?

A. 30 ft to 60 ftB. less than 60 ftC. greater than 60 ftD. 30 ft or 60 ft

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Complete parts a–c for each quadratic equation.

a. Find the value of the discriminant.b. Describe the number and type of roots.c. Find the exact solutions by using the Quadratic Formula.

10. 4x2 – 3x – 6 = 0

A.

; 2 irrational; B.

2 irrational; C.

105; 2 complex; D.

87; 2 irrational;

11. Consider the quadratic function f(x) = –2x2 + 3x + 8. Find the y-intercept and the equation of the axis of symmetry.A. The y-intercept is –8.

The equation of the axis of symmetry is x = .B.

The y-intercept is .The equation of the axis of symmetry is x = 8.

C. The y-intercept is 8.

The equation of the axis of symmetry is x = .D.

The y-intercept is .The equation of the axis of symmetry is x = –8.

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.

13. x2 + 11x + c

A.

B.

C.

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D.

Solve each inequality. Then graph the solution set on a number line.

15. 8x – 6 10

A. B.

C. D.

16. STOPPING DISTANCE The formula d = 0.05s2 + 1.1s estimates the minimum stoppingdistance d in feet for a car traveling s miles per hour. If a car stops in 200 feet, what is thefastest it could have been traveling when the driver applied the brakes?

A. about 15.4 mi/hB. about 75.6 mi/hC. about 53.2 mi/hD. about 53.2 mi/h

Factor the trinomial.

17. g2 – 9g – 22A. (g – 2)(g +

11)B. (g + 4)(g – 13)

C. (g – 23)(g + 1)

D. (g + 2)(g – 11)

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Solve the equation by graphing. If integral roots cannot be found, estimate the roots by stating the consecutive integers between which the roots lie.

18. –2 + 4 0A. between 2 and 0 and between 3 and –1 B. between 2 and –1 and between 0 and 3

C. between –2 and –3 and between 0 and 1 D.between 0 and –1 and between 2 and 3

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19. A. –1 and 1 B. between –3 and –4 and between –2 and –3

C. no real roots D. –4 and –2

Solve each equation by using the Square Root Property. Round to the nearest hundredth if necessary.

20. x2 – 14x + 49 = 9A. 7, 7B. 8, 5C. 4, 10D. –4, –10

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Simplify.

21. A.

B.

C.

D.

Graph the function.

22. A. B.

C. D.

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23. x2 – 3x + 2 0

A. {x | 1, 2}B. {x | x 1}C. {x | –1 x

3}D. {x | 1 x 2}

Factor each polynomial.

24. 8a2 + 2a – 6A. (8a – 6)(2a + 2)B. 2(4a – 3)(a + 1)C. 8(a – 3)(a + 1)D. 2(4a – 3)(a – 1)

Find the coordinates of the vertices of the figure formed by each system of inequalities.

25. y ≥ –62x + y ≤ 2y ≤ 2x + 2

A. (4, –6), (–4, –6), (0, 2)B. (4, 2), (0, –6), (–4, –6)C. (4, –6), (4, 6), (0, –2)D. (4, –6), (4, –6), (–1, –2)

Find the values of and m that make each equation true.

26. (6 – ) + (3m)i = –12 + 27i

A. = 9, m = 18B. = 18, m = 9C. = 6, m = 9D. = 1, m = 3

27. A square field has an area of 18,225 square feet. To the nearest foot, what is the diagonal distance across the field?A. 150 feet

B. 178 feet

C. 191 feet D. 212 feet

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Use the value of the discriminant to determine the number and type of roots for each equation to answer the following questions.

28. x2 – 3x + 7 = 0A. 2 complex roots B. 2 real, rational

rootsC. 2 real, irrational roots D. 1 real, rational root

29. Simplify (4 – 12i) – (–8 + 4i).A. 12 – 8 B. 28 C. 12 – 16i D. 12 + 16i

30. Find the exact solutions to 3x2 - 5x + 1 = 0 by using the Quadratic Formula.A. B. C. D.


31. 2x2 – 7x + 9 = 0A. 2 real,

rationalB. 2 real, irrational

C. 2 complex D. 1 real, rational

32. Solve –x2 = 4x by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

A. 4, 0 B. between –4 and 4C. –4, 0 D. –2, 4


33. 2x2 – 7x + 9 = 0A. 2 real,

rationalB. 2 real, irrational

C. 2 complex D. 1 real, rational

34. Write y = x2 + 4x – 1 in vertex form.A. y = (x – 2)2 + 5 B. y = (x + 2)2 – 5C. y = (x + 2)2 – 1 D. y = (x + 2)2 + 3

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35. By the Zero Product Property, if , then ____________.

A. B.

C. D.

36. What is the vertex of y = 2(x –3)2 + 6?A. (–3, –

6)B. (3, –6) C. (–3, 6) D. (3, 6)

37. Which quadratic equation has roots –2 and 3?A. x2 + x + 6 = 0 B. x2 – x – 6 = 0 C. x2 – 6x + 1 = 0 D. x2 + x – 6 = 0

38. To solve x2 + 8x + 16 = 25 by using the Square Root Property, you would first rewrite the equation as ____________.A. (x + 4)2 = 25 B. (x + 4)2 = 5C. x2 + 8x – 9 = 0 D. x2 + 8x = 9

39. Simplify (4 – 12i) – (–8 + 4i).A. 12 – 8 B. 28 C. 12 – 16i D. 12 + 16i

40. If , what is the value of ?A. –3 B.

C. D.

41. The quadratic equation x2 – 18x = –106 is to be solved by completing the square. Which equation would be a step in that solution?

A. (x – 9)2 = 25 B. x2 – 18x + 106 = 0C. x – 9 = ±5i D. x2 – 18x + 81 = –106

42. Write an equation for the parabola whose vertex is at (–8, 4) and passes through (–6, –2).A.

y = (x + 8)2 + 4B.

y = (x + 6)2 – 2C.

y = (x + 8)2 + 4D.

y = (x – 8)2 + 4

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Graph each function. State the domain and range.

43. A.

D = all real numbersR = y ≤ 0

B.

D = all real numbersR = y ≥ –2

C.

D = all real numbersR = y ≤ 0

D.

D = all real numbersR = y ≥ 2

44. Identify the quadratic function graphed below.

A. f (x) = –x2 – 2x B. f (x) = –x2 + 2xC. f (x) = x2 – 2x D. f (x) = –(x + 2)2

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45. Solve x2 2x + 24.A. {x | –4 x 6} B. {x | x –6 or x 4}C. {x | –6 x 4} D. {x | x –4 or x 6}

46. Which quadratic inequality is graphed below?

A. y (x – 2)(x + 3) B. y> (x – 2)(x + 3)

C. y> (x + 2)(x – 3)

D. y< (x + 2)(x – 3)

47. Solve x2 – 3x = 18 by factoring.A. {6} B. {–6, 3} C. {–9, 2} D. {–3, 6}

48. Solve (x – 4)(x + 2) ≤ 0.A. {x | x –2 or x 4} B. {x | –2 x 4}C. {x | –4 x 2} D. {x | x = –2 or x = 4}

49. The related graph of a quadratic equation is shown below. Use the graph to determine the solutions of the equation.

A. –2, 3

B. 0, –6

C. –3, 2

D. 0, 2


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A. f (x) = x2 – 4x B. f (x) = –x2 + 4xC. f (x) = –x2 – 4x D. f (x) = –(x + 4)2

53. If , then 8a equals which of the following?A. 1

6bB. 12b

C. D.

54. Identify the vertex, axis of symmetry, and direction of opening for y = (x – 8)2 + 2.A. (–8, 2); x = –8;

upB. (–8, –2); x = –8; down

C. (8, –2); x = 8; up D. (8, 2); x = 8; up

55. Solve .A. B.

C. D.

56. Mr. Salazár rented a car for d days. The rental agency charged x dollars per day plus c cents per mile for the model he selected. When Mr. Salazár returned the car, he paid a total of T dollars. In terms of d, x, c, and T, how many miles did he drive?

A. T – (xd + c) B.

C. D.


57. x2 + 20 = 12x – 16A. 1 real,

irrationalB. no real

C. 2 real, rational D. 1 real, rational


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A. f (x) = –x2 – 2x B. f (x) = –x2 + 2xC. f (x) = x2 – 2x D. f (x) = –(x + 2)2

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59. ELECTRICITY The total impedance of a series circuit is the sum of the impedances of all parts of the circuit. A technician determined that the impedance of the first part of a particular circuit was 2 + 5j ohms. The impedance of the remaining part of the circuit was 3 – 2j ohms. What was the total impedance of the circuit?

A. 5 + 3j ohms

B. 5 + 7j ohms

C. –1 + 7j ohms D. 16 + 11j ohms

60. What is the solution of ?A. {–11, 1} B. {–1, 11}C. D.

61. The window of a building is in the shape of a parabola that can be modeled by the equation where h(w) is the height of the window and w is the width in feet. Find the width of the window at a height of 8 feet.

63. If the area of the square shown below is square meters, what is the area of the rectangle in terms of x?

64. Determine whether has a maximum or a minimum value and find that value.

65. The sum of the ages of Anna, Emma, and Karen is 27 years. Anna is 2 years older than Karen, and Emma is 4 years younger than Anna. Write a system of equations that represents the ages of Anna, Emma, and Karen.

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66. A rock is thrown skyward from a cliff. The vertical distance in feet between the ground and the rock

t seconds after it is thrown can be determined by the equation How long will the rock take to hit the ground?

Write the function and state the domain and range.

70. Solve (x –1)2 0.

Solve each equation by factoring.

72.

Solve each equation by factoring.

73.

74. Alicia’s backyard is 12 feet longer than it is wide. The area covered by the backyard is not more than 288 square feet. What could the dimensions of Alicia’s backyard be?

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75. Graph y x2 – 4x + 4.

Solve the equation by completing the square.

76. 2x2 + 3x – 2 = 0

80. The width of a box is 1 inch less than its height. The length of the box is 4 inches more than its height. If the box has a volume of 12 cubic inches, what are the dimensions of the box?

Graph each function. State the domain and range.

82. f(x) = x + 1

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85. When you multiply a number by 4 and then subtract 7, the result is the same as if you first subtracted 7 from the same number and then multiplied by 11. What is the number?

Simplify.

88.

89. The height of a stone thrown with an initial speed of 15 meters per second from a cliff 490 meters above the ground is

given by the function The related quadratic equation is . Find the discriminant.

Bonus: Write a quadratic equation with roots ± .

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Solving Non-Linear Equations - Edl Web viewIf false, replace the underlined word or words to make a true sentence. 4. is an example of a quadratic equation. 5. In , the constant term