5-4 Completing the Square - Wikispaces - KMKunz

Name _______________________________________ Date __________________ Class __________________ LESSON

5-4

Practice A Completing the Square

Solve each equation using square roots. 1. x  12  9

2. x  22  16

x  1  ____

3. x  32  25

x  2  ____

________________________

x  3  _____

________________________

________________________

2

b To complete the square of x 2  bx , add   to the expression. Write 2 the term needed to complete the square for each expression.

4. x2  4x

5. x2  2x

________________________

6. x2  8x

________________________

________________________

Solve each equation by completing the square. 7. x2  10x  20 2

b a. Add   to each side of the equation. 2

x2  10x  _____  20  _______

b. Simplify.

x2  10x  ____  20  ____

c. Factor the square.

 x  ___  x  ___ 

d. Take square root of both sides.

x  _____ 

 ____

____

x  __________

e. Solve for x. 8. x  6x  23  0

9. x  13  14x

2

2

________________________________________

________________________________________

Solve. 10. Ralph and Edie each solved the equation x  72  100  0. Ralph says the correct answer is x  17. Edie says the correct answer is x  3. Who is correct? How do you know?

________________________________________________________________________________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

5-28

Holt Algebra 2

Name _______________________________________ Date __________________ Class __________________ LESSON

5-4

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

________________________________________

11. hx  3x  6x  15

________________________________________

12. f x  2x2  16x  4

2

________________________________________

_________________________________________

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.

5-28

Holt Algebra 2

Name _______________________________________ Date __________________ Class __________________ LESSON

5-4

Practice C Completing the Square

Complete the square for each expression. Write the resulting expression as a binomial squared. 1. x2  22x  _____

2. x2  9x  _____

________________________________________

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Solve each equation by completing the square. 3. 14x  x2  24

4. 2x2  8x  2

________________________________________

________________________________________

5. x  3x  4

6. 4x2  32x  16  0

2

________________________________________

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Write each function in vertex form, and identify its vertex. 8. g  x   x 2 

7. f x  x2  4x  17

________________________________________

9. hx  3x2  24x  15

1 x 1 2

________________________________________

10. f x  x2  3x  12

________________________________________

__________________________________________

Solve. 11. Write a quadratic equation with the vertex 3, 1 and a  1 in standard form. 12. What is the y-intercept for the graph of the function f x  2x  22  9? 13. The value of a stock is given by St  t 2  6t  13, where t is the number of days after the purchase. a. Complete the square and write the function in vertex form. b. What is the value of the stock at t  0? At what other time will the stock have this same value? c. What is the vertex? What does the vertex represent in terms of the stock price?

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

5-29

Holt Algebra 2

Practice C

Practice A

9  x  2   4. x  2  3

81 2. ; 4

1. 121; x  11

2

1.

9

x  1  3, x  4 or 2 2.

3. x  7 

16

5. x  1, 4

x  2  4, x  2 or 6 3.

73

2

6. x  4  2 3

7. fx  x  2  21, 2, 21 2

25

2

1 15  1 15   8. g  x    x    ; , 4 16  4 16  

x  3  5, x  8 or 2 2

4 4.    4 2 2

 8  6.   16  2 

2

9. hx  3x  42  33; 4, 33

2 5.    1 2

2

3 57  3 57   10. f  x     x    ;  , 2 4  2 4   11. fx  x2  6x  10 12. y-intercept  17 13. a. St  t  32  4

2

 10  7. a.   ;  2 

2

 10   2    b. 25; 25

b. 13; t  6 c. 3, 4; the minimum price

c. 5; 5; 45 d. 5;

45

e. 5  3 5 8. x  3  4 2

9. x  13, 1

10. They are both correct. Possible answer: A quadratic can have two possible solutions; x  7  10, so x  3, 17. Practice B 1. x  2 6

2. x  7  3 2

3. 4; x  2 5 41 5. d   2 2

4. 36; x  62

7. x  3  19

8. x  

2

6. x  3, 1 3 13  2 2

9. fx  x  32  11; 3, 11 10. gx  x  22  3; 2, 3 11. hx  3x  12  18; 1, 18 12. fx  2x  42  36; 4, 36 13. a. Base  8 ft, height  20 ft b. Base  10 ft, height  16 ft

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A56

Holt Algebra 2