Chapter 5 Quadratic Functions - 5.6 The Quadratic Formula And The Discriminant Worksheet Template Page 7
ADVERTISEMENT
1
2
3
4
5
6
7
8Page 1 of 2
77.
V
In a volleyball game, a player on one team spikes the ball
OLLEYBALL
over the net when the ball is 10 feet above the court. The spike drives the ball
downward with an initial vertical velocity of º55 feet per second. Players on
the opposing team must hit the ball back over the net before the ball touches
the court. How much time do the opposing players have to hit the spiked ball?
78.
A
The length l (in feet) of runway needed for a small airplane
VIATION
2
to land is given by l = 0.1s
º 3s + 22 where s is the airplane’s speed (in feet
per second). If a pilot is landing a small airplane on a runway 2000 feet long,
what is the maximum speed at which the pilot can land?
79.
T
For the years 1989–1996, the amount A (in
ELECOMMUNICATIONS
billions of dollars) spent on long distance telephone calls in the United States
2
can be modeled by A = 0.560t
+ 0.488t + 51 where t is the number of years
since 1989. In what year did the amount spent reach $60 billion?
DATA UPDATE
of Statistical Abstract of the United States data at
E
S
The volcanic cinder cone Puu Puai in Hawaii was formed
80.
ARTH
CIENCE
in 1959 when a massive “lava fountain” erupted at Kilauea Iki Crater, shooting
lava hundreds of feet into the air. When the eruption was most intense, the height
h (in feet) of the lava t seconds after being ejected from the ground could be
2
modeled by h = º16t
+ 350t.
Source: Volcano World
What was the initial vertical velocity of the lava? What was the lava’s
a.
maximum height above the ground?
C
M
For how long was the lava in the air? Solve the
b.
HOOSING A
ETHOD
problem either by factoring or by using the quadratic formula.
Test
Q
C
In Exercises 81–83, choose the statement that
UANTITATIVE
OMPARISON
is true about the given quantities.
Preparation
¡
The quantity in column A is greater.
A
¡
The quantity in column B is greater.
B
¡
The two quantities are equal.
C
¡
The relationship cannot be determined from the given information.
D
Column A
Column B
2
2
81.
Discriminant of x
º 6x º 1 = 0
Discriminant of x
+ 5x º 4 = 0
2
2
Discriminant of x
+ 2kx + 1 = 0
Discriminant of kx
+ 3x º k = 0
82.
2
2
83.
Least zero of ƒ(x) = x
º 10x + 23
Greatest zero of ƒ(x) = x
º 2x º 2
Challenge
T
R
The Stratosphere Tower in Las Vegas is 921 feet tall and has
84.
HRILL
IDES
a “needle” at its top that extends even higher into the air. A thrill ride called the
Big Shot catapults riders 160 feet up the needle and then lets them fall back to
the launching pad.
Source: Stratosphere Tower
a.
The height h (in feet) of a rider on the Big Shot can be modeled by
2
h = º16t
+ v
t + 921 where t is the elapsed time (in seconds) after launch
0
and v
is the initial vertical velocity (in feet per second). Find v
using the fact
0
0
that the maximum value of h is 921 + 160 = 1081 feet.
A brochure for the Big Shot states that the ride up the needle takes 2 seconds.
b.
2
E
C
XTRA
HALLENGE
Compare this time with the time given by the model h = º16t
+ v
t + 921
0
where v
is the value you found in part (a). Discuss the model’s accuracy.
0
5.6 The Quadratic Formula and the Discriminant
297
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education