Name ________________________________________ Date ___________________ Class __________________
LESSON
9-5
Challenge
Through the Tunnel
A parabolic tunnel is to be built for a two-lane road. The
Department of Transportation (DOT) wants the tunnel to be
wide enough for the two lanes and a walkway on either side.
An architect proposes a design that uses y = −0.08x2 + 2.88x
to model the height of the ceiling in feet at a distance x feet
from the bottom left. Your task is to determine whether the
design will satisfy all of the DOT’s requirements.
Use a graphing calculator as necessary.
1. What is the width of the tunnel from the bottom left to
the bottom right? Explain how you solved this problem.
____________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
2. According to state law, the maximum height of any vehicle
is 13.5 ft. To the nearest foot, how close to the bottom left
or bottom right could the tallest vehicle drive? Explain how
you found your answer.
____________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
3. According to state law, the standard width for one lane of
road is 12 ft. Is the tunnel wide enough for two lanes? Is it
wide enough for three lanes? Explain.
____________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
4. For the safety of pedestrians on the walkways, a 2-ft-wide
wall will be built between the outside edges of the road and
the walkways. If only two lanes are put in the middle of the
tunnel, how much room is left on either side for the walkway? ____________________________
5. Considering your answer to problem 4, will the ceiling of the
walkways be tall enough for an “average” pedestrian to walk
through? Explain.
____________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
6. Should the DOT accept or reject the architect’s design?
____________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
9-40
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