Download Extra Practice Worksheets 2.4-2.7

Name ________________________________________ Date __________________ Class__________________
LESSON
2-4
Practice B
Completing the Square
Solve each equation.
1. 2x2 6 42
2. x2 14x 49 18
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Complete the square for each expression. Write the resulting
expression as a binomial squared.
3. x2 4x _____
4. x2 12x _____
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Solve each equation by completing the square.
5. 2d 2 8 10d
6. x2 2x 3
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7. 3x2 18x 30
8. 4x2 12x 4
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Write each function in vertex form, and identify its vertex.
9. f x x2 6x 2
10. f x x2 4x 1
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2
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12. f x 2x2 16x 4
11. hx 3x 6x 15
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Solve.
13. Nathan made a triangular pennant for the band booster club. The area of the
pennant is 80 square feet. The base of the pennant is 12 feet shorter than the
height.
a. What are the lengths of the base and height of the pennant?
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b. What are the dimensions of the pennant if the base is only 6 feet shorter than the height?
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
2-5
Practice B
Complex Numbers and Roots
Express each number in terms of i.
1.
2. 2 18
32
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3.
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1
9
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Solve each equation.
4. 3x2 81 0
5. 4x2 28
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6.
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1 2
x 12 0
4
7. 6x2 126
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Find the values of x and y that make each equation true.
8. 2x 20i 8 4yi
9. 5i 6x 10yi 2
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Find the zeros of each function.
10. f x x2 2x 4
11. gx x2 6x 14
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Find each complex conjugate.
12. i 3
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13. 3i 4
14. 11i
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Solve.
15. The impedance of an electrical circuit is a way of measuring how much the
circuit impedes the flow of electricity. The impedance can be a complex
number. A circuit is being designed that must have an impedance that
satisfies the function f x 2x2 12x 40, where x is a measure of the
impedance. Find the zeros of the function.
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-36
Holt McDougal Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
2-6
Practice B
The Quadratic Formula
Find the zeros of each function by using the Quadratic Formula.
1. fx x2 10x 9
2. gx 2x2 4x 12
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3. h x 3 x 2 3 x 3
4
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4. f x x2 2x 3
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2
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6. gx x2 5x 3
5. gx 2x 3x 1
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Find the type and number of solutions for each equation.
7. x2 3x 8
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8. x2 4x 3
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9. 2x2 12x 18
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Solve.
10. A newspaper delivery person in a car is tossing folded newspapers from
the car window to driveways. The speed of the car is 30 feet per second,
and the driver does not slow down. The newspapers are tossed horizontally
from a height of 4 feet above the ground. The height of the papers as they
are thrown can be modeled by y 16t 2 4, and the distance they travel to
the driveway is d 30t.
a. How long does it take for a newspaper to land?
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b. From how many feet before the driveway must the papers be thrown?
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c. The delivery person starts to throw the newspapers at an angle and the height
of the papers as they travel can now be modeled by y 16t 2 12t 4.
How long does it take the papers to reach the ground now?
_________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-44
Holt McDougal Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
2-7
Practice B
Solving Quadratic Inequalities
Graph each inequality.
1. y x2 2x 6
2. y 2x2 x 7
Solve each inequality by using tables or graphs.
3. x2 3x 14 14
4. x2 9x 18
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Solve each inequality by using algebra.
5. x2 x 3 x
6. x2 6x 3 2
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7. 3 x 8x 15
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8. 3x2 x 8 12
2
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Solve.
9. An online music service that sells song downloads models its profit
using the function Pd 5d 2 450d 1000, where d is the number of
downloads sold and P is the profit. How many downloads does it need to
sell to make a profit of more than $8000?
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Algebra 2