Problem Solving
Name ________________________________________ Date ___________________ Class __________________ LESSON
9-5
Problem Solving Solving Quadratic Equations by Graphing
The path of a certain firework in the air is modeled by the parabolic function y = −16x2 + 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.
________________________________________ ________________________________________
4. What is the meaning of each of the zeros you found in problem 3? ________________________________________ ________________________________________
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) = −16x2 + 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 by the function y = −16x2 + 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?
7. The function y = −0.04x2 + 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
A 0.5 seconds
C 2 seconds
B 1.75 seconds
D 3.5 seconds
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
9-41
Holt McDougal Algebra 1
2. 6 ft; Solve 13.5 = 0.08x 2 + 2.88x by graphing y = 0.08x 2 + 2.88x 13.5. The zeros are approximately 6 and 30.
5. 2 seconds
3. yes; no; Two lanes require 24 ft, which is exactly the width that is taller than 13.5 ft. Three lanes require 36 ft; the cars in the outside lanes would hit the tunnel walls. 4. 4 ft 5. Yes; Evaluate y = 0.08x 2 + 2.88x when x = 4 to find y = 10.24. Because an “average” pedestrian is shorter than 10 ft, the walkway will be tall enough. 6. accept Problem Solving
Review for Mastery
1.
1. 0, 3; x = 0 3(0)2 + 9(0); 0 3(0) + 0; 0 0; 0 x = 3 3(3)2 + 9(3); 0 3(9) + (27); 0 27 + 27; 0 0; 0 2. 2; x = 2 (2)2 – 4(2) + 4; 0 4 8 + 4; 0 0; 0
2. 8 seconds; 400 feet 3. x = 3; x = 13
3. 0, 3; x = 0 2(0)2 + 6(0); 0 2(0) + 0; 0 0; 0 x=3 2(3)2 + 6(3); 0 2(9) + 18; 0 18 + 18; 0 0; 0
4. The firework launches at 3s; The firework lands at 13s 5. B
6. D
7. H Reading Strategies 1. quadratic function 2. y = 5x 2 + 7x; f(x) = 5x 2 + 7x
4. about 3.5 seconds
3. Because the graph may look like it intersects a point, but actually only come close to it.
5. about 24.5 seconds 6. about 5.5 seconds Challenge 1. 36 ft; Solve 0 = 0.08x 2 + 2.88x by graphing on a graphing calculator. The zeros are 0 and 36.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A31
Holt McDougal Algebra 1
9-5
Problem Solving Solving Quadratic Equations by Graphing
The path of a certain firework in the air is modeled by the parabolic function y = −16x2 + 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.
________________________________________ ________________________________________
4. What is the meaning of each of the zeros you found in problem 3? ________________________________________ ________________________________________
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) = −16x2 + 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 by the function y = −16x2 + 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?
7. The function y = −0.04x2 + 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
A 0.5 seconds
C 2 seconds
B 1.75 seconds
D 3.5 seconds
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
9-41
Holt McDougal Algebra 1
2. 6 ft; Solve 13.5 = 0.08x 2 + 2.88x by graphing y = 0.08x 2 + 2.88x 13.5. The zeros are approximately 6 and 30.
5. 2 seconds
3. yes; no; Two lanes require 24 ft, which is exactly the width that is taller than 13.5 ft. Three lanes require 36 ft; the cars in the outside lanes would hit the tunnel walls. 4. 4 ft 5. Yes; Evaluate y = 0.08x 2 + 2.88x when x = 4 to find y = 10.24. Because an “average” pedestrian is shorter than 10 ft, the walkway will be tall enough. 6. accept Problem Solving
Review for Mastery
1.
1. 0, 3; x = 0 3(0)2 + 9(0); 0 3(0) + 0; 0 0; 0 x = 3 3(3)2 + 9(3); 0 3(9) + (27); 0 27 + 27; 0 0; 0 2. 2; x = 2 (2)2 – 4(2) + 4; 0 4 8 + 4; 0 0; 0
2. 8 seconds; 400 feet 3. x = 3; x = 13
3. 0, 3; x = 0 2(0)2 + 6(0); 0 2(0) + 0; 0 0; 0 x=3 2(3)2 + 6(3); 0 2(9) + 18; 0 18 + 18; 0 0; 0
4. The firework launches at 3s; The firework lands at 13s 5. B
6. D
7. H Reading Strategies 1. quadratic function 2. y = 5x 2 + 7x; f(x) = 5x 2 + 7x
4. about 3.5 seconds
3. Because the graph may look like it intersects a point, but actually only come close to it.
5. about 24.5 seconds 6. about 5.5 seconds Challenge 1. 36 ft; Solve 0 = 0.08x 2 + 2.88x by graphing on a graphing calculator. The zeros are 0 and 36.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A31
Holt McDougal Algebra 1
