Practice B Solving Quadratic Equations by Factoring
Use the Zero Product Property to solve each equation. Check your answers. 1. x ⫺ 1 x ⫺ 5 ⫽ 0 x⫺1⫽0 x⫽
or or
2. x ⫺ 2 x ⫺ 9 ⫽ 0 x⫺5⫽0 x⫽
x⫺2⫽0 x ⫽
3. x ⫺ 2 x ⫹ 4 ⫽ 0
or x ⫺ 9 ⫽ 0 or x ⫽
4. 2x ⫹ 1 x ⫺ 6 ⫽ 0
Solve each quadratic equation by factoring. 2 5. x ⫺ 3x ⫽ 0
6. x 2 ⫹ 4x ⫹ 3 ⫽ 0
7. x 2 ⫹ 5x⫺ 6 ⫽ 0
8. x 2 ⫹ 11x ⫹ 24 ⫽ 0
9. x 2 ⫺ 12x ⫹ 11 ⫽ 0
10. x 2 ⫹ 18x ⫺ 65 ⫽ 0
11. x 2 ⫺ 4x ⫺ 12 ⫽ 0
12. x 2 ⫹ 11x ⫹ 10 ⫽ 0
13. x 2 ⫹ 12x ⫹ 35 ⫽ 0
14. 2x 2 ⫺ 3x ⫺ 5 ⫽ 0
15. 3x 2 ⫺ 5x ⫺ 2 ⫽ 0
16. x 2 ⫽ 3x ⫹ 40
17. x 2 ⫺ 14 ⫽ 5x
18. 2x ⫺ 1 ⫽ ⫺8x 2
19. x ⫽ 10x 2 ⫺ 2
20. 2x 2 ⫽ 13x ⫹ 7
21. 6x 2 ⫹ x ⫽ 5
22. x 2 ⫽ 5x
23. The height of a flare fired from the deck of a ship 2 in distress can be modeled by h ⫽ ⫺16t ⫹ 104t ⫹ 56, where h is the height of the flare above water and t is the time in seconds. Find the time it takes the flare to hit the water.
Solve using square roots. Check your answer. 2 1. x 81
2. x 2 100
x 兹 81
x
x
x
The solutions are 2 3. x 225
x 兹
and
.
兹
The solutions are
4. 441 x 2
9. 49x 2 64 0
12. 0 81x 2 121
.
5. x 2 400
兹
x
x
x 6. 3x 2 108
and
7. 100 4x 2
8. x 2 7 71
10. 2x 2 162
11. 9x 2 100 0
13. 100x 2 25
14. 100x 2 121
Solve. Round to the nearest hundredth. 2 15. 8x 56
16. 5 x 2 20
17. x 2 35 105
18. The height of a skydiver jumping out of an airplane is given 2 by h 16t 3200. How long will it take the skydiver to reach the ground? Round to the nearest tenth of a second. 19. The height of a triangle is twice the length of its base. The 2 area of the triangle is 50 m . Find the height and base to the nearest tenth of a meter. 20. The height of an acorn falling out of a tree is given 2 by h 16t b. If an acorn takes 1 second to fall to the ground. What is the value of b?
The path of a certain firework in the air is modeled by the parabolic 2 function y ⫽ ⫺16x ⫹ 256x ⫺ 624 where x is the number of seconds after the fuse is lit. Write the correct answer. 2. The firework will explode when it reaches its highest point. How long after the fuse is lit will the firework explode and how high will the firework be?
1. Graph the function on the grid below. &LIGHTOFTHE&IREWORK
(EIGHTFT
4. What is the meaning of each of the zeros you found in problem 3?
4IMES
3. Based on the graph of the firework, what are the two zeros of this function?
Select the best answer. 5. The quadratic function f x ⫽ ⫺16x 2 ⫹ 90x models the height of a baseball in feet after x seconds. How long is the baseball in the air? A 2.8125 s C 11.25 s B 5.625 s D 126.5625 s
6. The height of a football y in feet is given 2 by the function y ⫽ ⫺16x ⫹ 56x ⫹ 2 where x is the time in seconds after the ball was kicked. This function is graphed below. How long was the football in the air? (EIGHTOF&OOTBALL
2 7. The function y ⫽ ⫺0.04x ⫹ 2x models the height of an arch support for a bridge, where x is the distance in feet from where the arch supports enter the water. How many real solutions does this function have? F 0 H 2 G 1 J 3
Problem Solving Solving Quadratic Equations by Factoring
Write the correct answer. 1. The height of an acorn falling out of 2 a tree is h ⫽ ⫺16t ⫹ 25 where h is height in feet and t is time in seconds. Determine how long it takes the acorn to reach the ground. Check your answer by graphing the function.
2. An architect is designing a building with a right triangular footprint.
(EIGHTOF!CORN
The hypotenuse of the triangle is 80 feet longer than one leg of the triangle and 40 feet longer than the other leg. Use the Pythagorean Theorem to find the dimensions of the footprint of the building.
(EIGHTFT
4IMES
4. During a game of golf, Kayley hits her ball out of a sand trap. The equation 2 h ⫽ ⫺16t ⫹ 20t ⫺ 4 models the height of the golf ball in feet in relation to the number of t seconds since it was hit. Find how long it takes Kayley’s golf ball to reach to green.
3. Robert threw a rock off a bridge into the river. The distance from the rock to the river is modeled by the equation 2 h ⫽ ⫺16t ⫺ 16t ⫹ 60, where h is the height in feet and t is the time in seconds. Find how long it took the rock to enter the water.
A new store is being built in the shape of a rectangle with a parking lot in the shape of an isosceles trapezoid. The parking lot and the store will share a side as shown. Select the best answer. 5. The parking lot will have an area of 160 square meters. The shorter base is 4 m longer than the height of the trapezoid, and the longer base is 8 m longer than the height. What is the length of the shorter base? F 10 meters H 18 meters G 14 meters J 20 meters
7. What is the depth of the store in meters? F 7 H 14 G 11 J 28
65
Holt Algebra 1
3/27/06 7:35:42 PM
Name T E K S A.10.A
Date
Class
LESSON
Problem Solving
9-7
Solving Quadratic Equations by Using Square Roots
A furniture maker has designed a bookcase with the proportions shown in the diagram below. Write the correct answer. 1. A customer has requested a bookcase with the two shelves having a total area of 864 square inches. What should b equal to meet the customer’s specifications? B
B
2. Barnard has a stain on his wall and would like to cover it up with a bookcase. What should b equal in order for the back of the bookcase to cover an area of 4800 square inches?
B
3. Bria would like to display her collection of soap carvings on top of her bookcase. The collection takes up an area of 400 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
4. Eliana would like to cover the side panels with silk. She has 1600 square inches of silk. What should b equal so that she can use all of her silk to completely cover the sides? Round your answer to the nearest tenth of an inch.
Select the best answer. 5. Carter plans to wallpaper the longest wall in his living room. The wall is twice as long as it is high and has an area of 162 square feet. What is the height of the wall? A 8 feet C 12 feet B 9 feet D 18 feet
6. An apple drops off the apple tree from a height of 8 feet. How long does it take the apple to reach the ground? Use the 2 function f x ⫽ ⫺16x ⫹ c, where c is the initial height of a falling object, to find the answer. F 0.5 seconds G 0.71 seconds
7. Trinette cut a square tablecloth into 4 equal pieces that she used to make two pillow covers. The area of the tablecloth was 3600 square inches. What is the side length of each piece Trinette used to make the pillow covers? A 20 inches C 60 inches B 30 inches D 90 inches
8. Elton earns x dollars per hour at the 2 bookstore. His mother, Evelyn, earns x dollars per hour as a career counselor. Twice Evelyn’s wage equals $84.50. What is Elton’s hourly wage? Round your answer to the nearest cent. F $4.60 H $9.19 G $6.50 J $13.00
