Linear And Quadratic Functions Worksheet Page 3
ADVERTISEMENT
1
2
3
4
5
6
7
8
9210
Linear and Quadratic Functions
now? What is the maximum area? Assuming an average alpaca requires 25 square feet of
pasture, how many alpaca can he raise now?
21. What is the largest rectangular area one can enclose with 14 inches of string?
22. The height of an object dropped from the roof of an eight story building is modeled by
2
h(t) =
16t
+ 64, 0
t
2. Here, h is the height of the object off the ground, in feet, t
seconds after the object is dropped. How long before the object hits the ground?
23. The height h in feet of a model rocket above the ground t seconds after lift-off is given by
2
h(t) =
5t
+ 100t, for 0
t
20. When does the rocket reach its maximum height above
the ground? What is its maximum height?
24. Carl’s friend Jason participates in the Highland Games. In one event, the hammer throw, the
height h in feet of the hammer above the ground t seconds after Jason lets it go is modeled by
2
h(t) =
16t
+ 22.08t + 6. What is the hammer’s maximum height? What is the hammer’s
total time in the air? Round your answers to two decimal places.
25. Assuming no air resistance or forces other than the Earth’s gravity, the height above the
2
ground at time t of a falling object is given by s(t) =
4.9t
+ v
t + s
where s is in meters, t
0
0
is in seconds, v
is the object’s initial velocity in meters per second and s
is its initial position
0
0
in meters.
(a) What is the applied domain of this function?
(b) Discuss with your classmates what each of v
> 0, v
= 0 and v
< 0 would mean.
0
0
0
(c) Come up with a scenario in which s
< 0.
0
(d) Let’s say a slingshot is used to shoot a marble straight up from the ground (s
= 0) with
0
an initial velocity of 15 meters per second. What is the marble’s maximum height above
the ground? At what time will it hit the ground?
(e) Now shoot the marble from the top of a tower which is 25 meters tall. When does it hit
the ground?
(f) What would the height function be if instead of shooting the marble up off of the tower,
you were to shoot it straight DOWN from the top of the tower?
11
26. The two towers of a suspension bridge are 400 feet apart. The parabolic cable
attached to
the tops of the towers is 10 feet above the point on the bridge deck that is midway between
the towers. If the towers are 100 feet tall, find the height of the cable directly above a point
of the bridge deck that is 50 feet to the right of the left-hand tower.
2
27. Graph f (x) = 1
x
28. Find all of the points on the line y = 1
x which are 2 units from (1, 1).
11
The weight of the bridge deck forces the bridge cable into a parabola and a free hanging cable such as a power
line does not form a parabola. We shall see in Exercise
35
in Section
6.5
what shape a free hanging cable makes.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education