Practice Form g solve each equation by finding square roots



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Name

Class


Date





Completing the Square
4-6

Practice

Form G

Solve each equation by finding square roots.

1. 3x2 = 75 2. 5x2 45 = 0 3. 4x2 49 = 0

4. 6x2 = 216 5. 2x2 = 14 6. 3x2 96 = 0

7. A box is 4 in. high. Its length is 1.5 times its width. The volume of the box is 1350 in.2. What are the width and length of the box?

Solve each equation.

8. x2 + 12x + 36 = 25 9. x2 10x + 25 = 144

10. 11. x2 22x + 121 = 225

12. 16x2 + 8x + 1 = 16 13. 25x2 30x + 9 = 81

Complete the square.

14. x2 + 22x + 15. x2 30x + 16. x2 + 5x +

17. 18. 25x2+ 10x + 19. 4x2 12x +

Solve each quadratic equation by completing the square.

20. x2 + 10x 1 = 0 21. x2 + 2x 7 = 0

22. x2 + 6x + 10 = 0 23. x2 + 5x = 3x + 11

24. 3x2 + 4x = 2x2 + 3 25.

26. 0.2x2 + 0.4x + 0.8 = 0 27. 4x2 + 20x + 1 = 0


Prentice Hall Gold Algebra 2• Teaching Resources

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53

Name

Class


Date




4-6

Practice (continued)

Completing the Square

Form G



Rewrite each equation in vertex form.

28. y = x2 6x + 4 29. y = x2 + 14x + 50

30. y = 3x2 + 8x + 2 31. y = 2x2 + 6x 2

Find the value of k that would make the left side of each equation a perfect square trinomial.

32. x2 + kx + 196 = 0 33. 64x2 kx + 1 = 0

34. x2 kx + 16 = 0 35. 4x2 kx + 9 = 0

36. 16x2 + kx + 9 = 0 37.

38. The quadratic function d = t2 + 4t + 33 models the depth of water in a flood channel after a rainstorm. The time in hours after it stops raining is t and d is the depth of the water in feet.

  1. Solve the equation t2 + 4t + 33 = 0.

  2. Approximate the positive solution found in part (a) to two decimal places.

  3. Interpret the answer to part (b) in terms of the problem.

39. While in orbit, a space scientist measures the pressure inside a container as it is being heated and then cooled. She records the information and discovers the pressure p, in pounds per square inch, is related to the time t in minutes after the experiment begins according to the equation p = 0.2t2 + 1.6t.

  1. Complete the square in the expression 0.2t2 + 1.6t.

  2. Rewrite the equation for p in vertex form.

  3. What is a reasonable domain for this function? Explain.

  4. When does the maximum pressure occur? What is the maximum pressure?

Prentice Hall Gold Algebra 2 • Teaching Resources

Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.



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