Name _______________________________________ Date __________________ Class __________________ LESSON
5-4
Practice A Completing the Square
Solve each equation using square roots. 1. x 12 9
2. x 22 16
x 1 ____
3. x 32 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 72 100 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. hx 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 _____
________________________________________
________________________________________
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
________________________________________
________________________________________
Write each function in vertex form, and identify its vertex. 8. g x x 2
7. f x x2 4x 17
________________________________________
9. hx 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 2x 22 9? 13. The value of a stock is given by St 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. fx 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. hx 3x 42 33; 4, 33
2 5. 1 2
2
3 57 3 57 10. f x x ; , 2 4 2 4 11. fx x2 6x 10 12. y-intercept 17 13. a. St t 32 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 62
7. x 3 19
8. x
2
6. x 3, 1 3 13 2 2
9. fx x 32 11; 3, 11 10. gx x 22 3; 2, 3 11. hx 3x 12 18; 1, 18 12. fx 2x 42 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