Problem Solving
Name ________________________________________ Date __________________ Class__________________ LESSON
9-2
Problem Solving Characteristics of Quadratic Functions
Write the correct answer.
1. A superhero is trying to leap over a tall building. The function f(x) = −16x 2 + 200x gives the superhero’s height in feet as a function of time. The building is 612 feet high. Will the superhero make it over the building? Explain.
2. The graph shows the height of an arch support for a pedestrian bridge.
_________________________________________ _________________________________________ _________________________________________
3. The distance between the cables suspending a bridge and the water below is given by the function y = 0.02x 2 − 2x + 80. Find the vertex of the graph.
Find the zeros (if any) and axis of symmetry of this parabola. ____________________________________________
_________________________________________
____________________________________________
After a heavy snowfall, Joe and Karin made an igloo. The dome of the igloo is in the shape of a parabola and the height of the igloo in inches is given by f(x) = −0.03x2 + 2.4x. Select the best answer.
4. Joe wants to place a support in the middle of the igloo, along the axis of symmetry. How far from the edge of the igloo should he place the support? A 24 in.
C 48 in.
B 40 in.
D 80 in.
7. What is the vertex of the parabola that Karin graphed?
H 48 in.
G 40 in.
J 80 in.
6. Karin graphs the parabola and looks at the zeros to see how wide the igloo is. What are the zeros of this parabola? A −80 and 80
C 0 and 80
B −40 and 40
D 40 and 80
H (48, 40)
G (40, 48)
J (80, 0)
8. Which graph below is the graph that Karin made?
5. Neither Joe nor Karin can stand up inside the igloo. How tall is the center of the igloo? (Hint: the top of the igloo is the vertex of the parabola.) F 24 in.
F (20, 36)
A
C
B
D
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
9-17
Holt McDougal Algebra 1
4. x −2 −1 0 1 2
Practice C
y 8 2 0 2 8
1. −3 and 3
2. −6 and 0
3. no zeros
4. x = −3
5. x = 4
6. x = 1
7. x =
1 8
9. x = −
5.
3 8
11. (−2, 15)
8. x = −0.75 10. (1, −3) 3 17 12. (− , − ) 2 2
Review for Mastery
1. x = 3
2. x = 2
3. The axis of symmetry is x = −3. 4. The axis of symmetry is x = 0. 5. −10; 1; 10; 2; 5; x = 5 6. x = 1 7. x = 5; 5; 5; 0; y = 0; (5, 0)
6. (0, 0)
8. (1, 8)
7. upward; because a > 0.
9. The vertex is (−3, −27)
LESSON 9–2
Challenge
1. (−6, 0); (−3, −9); (0, 0)
Practice A
1. −4 and 0
2. −2
2. 0 = 36a − 6b + c; −9 = 9a − 3b + c; 0 = c
3. no zeros
4. x = 0
3. 1; 6; 0
5. x = −4
6. x = 5
⎧0 = 9a − 3b + c ⎪ 5. ⎨18 = c ; y = −2 x 2 + 18 ⎪0 = 9a + 3b + c ⎩
7. 1; 8; −4; x = −4; (−4, −4) 8. 1; −10; 5; x = 5; (5, 15) 9. 2; −8; 2; x = 2; (2, −11)
⎧0 = 25a − 5b + c ⎪ 6. ⎨0 = 4a + 2b + c ; y = x 2 + 3 x − 10 ⎪− 12.25 = 2.25a − 1.5b + c ⎩
Practice B
1. −6 and 1
2. no zeros
3. 5
4. x =
5. x = 3
6. x = −1
7. x = 1
8. x = 2
1 9. x = − 16 11. (−2, −22)
4. y = x 2 + 6x
7 2
Problem Solving
1. Yes; the vertex is (6.25, 625) and 625 > 612
10. (1, −5) 12. (−1, −36)
2. 0 and 50; x = 25
3. (50, 30)
4. B
5. H
6. C
7. G
8. D
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A22
Holt McDougal Algebra 1
9-2
Problem Solving Characteristics of Quadratic Functions
Write the correct answer.
1. A superhero is trying to leap over a tall building. The function f(x) = −16x 2 + 200x gives the superhero’s height in feet as a function of time. The building is 612 feet high. Will the superhero make it over the building? Explain.
2. The graph shows the height of an arch support for a pedestrian bridge.
_________________________________________ _________________________________________ _________________________________________
3. The distance between the cables suspending a bridge and the water below is given by the function y = 0.02x 2 − 2x + 80. Find the vertex of the graph.
Find the zeros (if any) and axis of symmetry of this parabola. ____________________________________________
_________________________________________
____________________________________________
After a heavy snowfall, Joe and Karin made an igloo. The dome of the igloo is in the shape of a parabola and the height of the igloo in inches is given by f(x) = −0.03x2 + 2.4x. Select the best answer.
4. Joe wants to place a support in the middle of the igloo, along the axis of symmetry. How far from the edge of the igloo should he place the support? A 24 in.
C 48 in.
B 40 in.
D 80 in.
7. What is the vertex of the parabola that Karin graphed?
H 48 in.
G 40 in.
J 80 in.
6. Karin graphs the parabola and looks at the zeros to see how wide the igloo is. What are the zeros of this parabola? A −80 and 80
C 0 and 80
B −40 and 40
D 40 and 80
H (48, 40)
G (40, 48)
J (80, 0)
8. Which graph below is the graph that Karin made?
5. Neither Joe nor Karin can stand up inside the igloo. How tall is the center of the igloo? (Hint: the top of the igloo is the vertex of the parabola.) F 24 in.
F (20, 36)
A
C
B
D
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
9-17
Holt McDougal Algebra 1
4. x −2 −1 0 1 2
Practice C
y 8 2 0 2 8
1. −3 and 3
2. −6 and 0
3. no zeros
4. x = −3
5. x = 4
6. x = 1
7. x =
1 8
9. x = −
5.
3 8
11. (−2, 15)
8. x = −0.75 10. (1, −3) 3 17 12. (− , − ) 2 2
Review for Mastery
1. x = 3
2. x = 2
3. The axis of symmetry is x = −3. 4. The axis of symmetry is x = 0. 5. −10; 1; 10; 2; 5; x = 5 6. x = 1 7. x = 5; 5; 5; 0; y = 0; (5, 0)
6. (0, 0)
8. (1, 8)
7. upward; because a > 0.
9. The vertex is (−3, −27)
LESSON 9–2
Challenge
1. (−6, 0); (−3, −9); (0, 0)
Practice A
1. −4 and 0
2. −2
2. 0 = 36a − 6b + c; −9 = 9a − 3b + c; 0 = c
3. no zeros
4. x = 0
3. 1; 6; 0
5. x = −4
6. x = 5
⎧0 = 9a − 3b + c ⎪ 5. ⎨18 = c ; y = −2 x 2 + 18 ⎪0 = 9a + 3b + c ⎩
7. 1; 8; −4; x = −4; (−4, −4) 8. 1; −10; 5; x = 5; (5, 15) 9. 2; −8; 2; x = 2; (2, −11)
⎧0 = 25a − 5b + c ⎪ 6. ⎨0 = 4a + 2b + c ; y = x 2 + 3 x − 10 ⎪− 12.25 = 2.25a − 1.5b + c ⎩
Practice B
1. −6 and 1
2. no zeros
3. 5
4. x =
5. x = 3
6. x = −1
7. x = 1
8. x = 2
1 9. x = − 16 11. (−2, −22)
4. y = x 2 + 6x
7 2
Problem Solving
1. Yes; the vertex is (6.25, 625) and 625 > 612
10. (1, −5) 12. (−1, −36)
2. 0 and 50; x = 25
3. (50, 30)
4. B
5. H
6. C
7. G
8. D
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A22
Holt McDougal Algebra 1
