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Name ________________________________________ Date __________________ Class__________________ LESSON 2-4 Practice B Completing the Square Solve each equation. 1. 2x2 6 42 2. x2 14x 49 18 _________________________________________ ________________________________________ Complete the square for each expression. Write the resulting expression as a binomial squared. 3. x2 4x _____ 4. x2 12x _____ _________________________________________ ________________________________________ Solve each equation by completing the square. 5. 2d 2 8 10d 6. x2 2x 3 _________________________________________ ________________________________________ 7. 3x2 18x 30 8. 4x2 12x 4 _________________________________________ ________________________________________ Write each function in vertex form, and identify its vertex. 9. f x x2 6x 2 10. f x x2 4x 1 _________________________________________ 2 ________________________________________ 12. f x 2x2 16x 4 11. hx 3x 6x 15 _________________________________________ __________________________________________ 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? _________________________________________________________________________________________ b. What are the dimensions of the pennant if the base is only 6 feet shorter than the height? _________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 2-28 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 ________________________ 3. _________________________ 1 9 ________________________ Solve each equation. 4. 3x2 81 0 5. 4x2 28 _________________________________________ 6. ________________________________________ 1 2 x 12 0 4 7. 6x2 126 _________________________________________ ________________________________________ Find the values of x and y that make each equation true. 8. 2x 20i 8 4yi 9. 5i 6x 10yi 2 _________________________________________ ________________________________________ Find the zeros of each function. 10. f x x2 2x 4 11. gx x2 6x 14 _________________________________________ ________________________________________ Find each complex conjugate. 12. i 3 ________________________ 13. 3i 4 14. 11i _________________________ ________________________ 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. _________________________________________________________________________________________ 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 _________________________________________ 3. h x 3 x 2 3 x 3 4 ________________________________________ 4. f x x2 2x 3 _________________________________________ 2 ________________________________________ 6. gx x2 5x 3 5. gx 2x 3x 1 _________________________________________ ________________________________________ Find the type and number of solutions for each equation. 7. x2 3x 8 ________________________ 8. x2 4x 3 _________________________ 9. 2x2 12x 18 ________________________ 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? _________________________________________________________________________________________ b. From how many feet before the driveway must the papers be thrown? _________________________________________________________________________________________ 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 _________________________________________ ________________________________________ Solve each inequality by using algebra. 5. x2 x 3 x 6. x2 6x 3 2 _________________________________________ 7. 3 x 8x 15 ________________________________________ 8. 3x2 x 8 12 2 _________________________________________ ________________________________________ 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? _________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 2-52 Holt McDougal Algebra 2