Practice 4-6 Form G Solve each equation by finding square roots. 1. ... Solve each quadratic equation by completing the square. 20. x 2 + 10x 1 = 0 21...
1 Lesson 5.4--Completing the Square Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you
5-4 Completing the Square LESSON You can use the square root property to solve some quadratic equations. Square Root Property To solve x 2 a, take the square root
Practice C Completing the Square Complete the square for each expression. Write the resulting expression as a binomial squared. ... 4 5. 2 2 2 1 6. 2 8 2
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LESSON Problem Solving 5-4 Completing the Square Sean and Mason run out of gas while fishing from their boat in the ... c. Solve the equation by completing the square
Practice B Completing the Square Solve each equation. 1. 2 x 2 6 42 2. x 2 14x 49 18 Complete the square for each expression. Write the resulting
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Name
Class
4-6
Date
Practice
Form G
Completing the Square
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. 9. x2 10x + 25 = 144
8. x2 + 12x + 36 = 25 10. x 2 6 x 9
49 4
11. x2 22x + 121 = 225 13. 25x2 30x + 9 = 81
12. 16x2 + 8x + 1 = 16
Complete the square. 14. x2 + 22x + 17. x 2
1 x 2
15. x2 30x +
16. x2 + 5x +
18. 25x2+ 10x +
19. 4x2 12x +
Solve each quadratic equation by completing the square. 20. x2 + 10x 1 = 0
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.
1 2 1 x kx 0 4 25
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. a. Solve the equation t2 + 4t + 33 = 0. b. Approximate the positive solution found in part (a) to two decimal places. c. 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. a. Complete the square in the expression 0.2t2 + 1.6t. b. Rewrite the equation for p in vertex form. c. What is a reasonable domain for this function? Explain. d. When does the maximum pressure occur? What is the maximum pressure?
