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Extracting Square Roots
Solve by extracting the roots.
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Find a quadratic equation in standard form with the given solutions.
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Completing the Square
Complete the square.
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Solve by completing the square.
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Quadratic Formula
Identify the coefficients a, b, and c used in the quadratic formula. Do not solve.
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Use the quadratic formula to solve the following.
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Guidelines for Solving Quadratic Equations and Applications
Use the discriminant to determine the number and type of solutions.
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Solve using any method.
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Set up an algebraic equation and use it to solve the following.
63. The length of a rectangle is 2 inches less than twice the width. If the area measures 25 square inches, then find the dimensions of the rectangle. Round off to the nearest hundredth.
64. An 18-foot ladder leaning against a building reaches a height of 17 feet. How far is the base of the ladder from the wall? Round to the nearest tenth of a foot.
65. The value in dollars of a new car is modeled by the function , where t represents the number of years since it was purchased. Determine the age of the car when its value is $22,000.
66. The height in feet reached by a baseball tossed upward at a speed of 48 feet/second from the ground is given by the function , where t represents time in seconds. At what time will the baseball reach a height of 16 feet?
Graphing Parabolas
Determine the x- and y-intercepts.
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Find the vertex and the line of symmetry.
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Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist.
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Determine the maximum or minimum y-value.
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87. The value in dollars of a new car is modeled by the function , where t represents the number of years since it was purchased. Determine the age of the car when its value is at a minimum.
88. The height in feet reached by a baseball tossed upward at a speed of 48 feet/second from the ground is given by the function , where t represents time in seconds. What is the maximum height of the baseball?
Introduction to Complex Numbers and Complex Solutions
Rewrite in terms of i.
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Perform the operations.
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Solve.
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Solve by extracting the roots.
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Solve by completing the square.
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Solve using the quadratic formula.
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Solve using any method.
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Set up an algebraic equation and solve.
11. The length of a rectangle is twice its width. If the diagonal measures centimeters, then find the dimensions of the rectangle.
12. The height in feet reached by a model rocket launched from a platform is given by the function , where t represents time in seconds after launch. At what time will the rocket reach 451 feet?
Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist.
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17. Determine the maximum or minimum y-value: .
18. Determine the x- and y-intercepts: .
19. Determine the domain and range: .
20. The height in feet reached by a model rocket launched from a platform is given by the function , where t represents time in seconds after launch. What is the maximum height attained by the rocket.
21. A bicycle manufacturing company has determined that the weekly revenue in dollars can be modeled by the formula , where n represents the number of bicycles produced and sold. How many bicycles does the company have to produce and sell in order to maximize revenue?
22. Rewrite in terms of i: .
23. Divide: .
Solve.
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1: ±16
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7: 2, 8
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23: −3/2, 1
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31: , , and
33: , , and
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43: −12, 24
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47: Two real solutions
49: One real solution
51: −10, 6
53: ±1/5
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59: −4, 3
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63: Length: 6.14 inches; width: 4.07 inches
65: It is worth $22,000 new and when it is 24 years old.
67: x-intercepts: (−3, 0), (1/2, 0); y-intercept: (0, −3)
69: x-intercepts: none; y-intercept: (0, 2)
71: Vertex: (3, −8); line of symmetry:
73: Vertex: (−3/2, −13/4); line of symmetry:
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83: Minimum: y = −24
85: Maximum: y = 9/5
87: The car will have a minimum value 12 years after it is purchased.
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5: −1, 3/2
7: −6/5, 0
9: −2, −1
11: Length: 12 centimeters; width: 6 centimeters
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17: Maximum: y = −3
19: Domain: R; range:
21: To maximize revenue, the company needs to produce and sell 100 bicycles a week.
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