Chapter 5 Quadratic Functions - 5.6 The Quadratic Formula And The Discriminant Worksheet Template Page 6
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S
A
M
Solve the equation by factoring, by finding
OLVING BY
NY
ETHOD
square roots, or by using the quadratic formula.
2
2
46.
6x
º 12 = 0
47.
x
º 3x º 15 = 0
2
2
x
+ 4x + 29 = 0
x
º 18x + 32 = 0
48.
49.
2
2
50.
4x
+ 28x = º49
51.
3(x + 4)
= º27
2
2
2
2
º2u
+ 5 = 3u
º 10u
11m
º 1 = 7m
+ 2
52.
53.
2
2
2
54.
º9v
+ 35v º 30 = 1 º v
55.
20p
+ 6p = 6p
º 13p + 3
U
D
Find the discriminant of the quadratic equation
SING THE
ISCRIMINANT
and give the number and type of solutions of the equation.
2
2
2
x
º 4x + 10 = 0
x
+ 3x º 6 = 0
x
+ 14x + 49 = 0
56.
57.
58.
2
2
2
59.
3x
º 10x º 5 = 0
60.
64x
º 16x + 1 = 0
61.
º2x
º 5x º 4 = 0
2
2
2
7r
º 3 = 0
s
5 + s + 5 = 0
º4t
+ 20t º 25 = 0
62.
63.
64.
V
T
In Exercises 65–67, the graph of a quadratic function
ISUAL
HINKING
2
2
y = ax
+ bx + c is shown. Tell whether the discriminant of ax
+ bx + c = 0
is positive, negative, or zero.
65.
66.
67.
y
y
y
x
x
x
T
C
T
Find all values of c for which the equation has (a) two
HE
ONSTANT
ERM
real solutions, (b) one real solution, and (c) two imaginary solutions.
F
OCUS ON
C
AREERS
2
2
2
68.
x
º 2x + c = 0
69.
x
+ 4x + c = 0
70.
x
+ 10x + c = 0
2
2
2
x
º 8x + c = 0
x
+ 6x + c = 0
x
º 12x + c = 0
71.
72.
73.
2
C
T
Explain why the height model h = º16t
+ v
t + h
74.
RITICAL
HINKING
0
0
applies not only to launched or thrown objects, but to dropped objects as well.
(Hint: What is the initial vertical velocity of a dropped object?)
D
In July of 1997, the first Cliff Diving World Championships were
75.
IVING
held in Brontallo, Switzerland. Participants performed acrobatic dives from
heights of up to 92 feet. Suppose a cliff diver jumps from this height with an
initial upward velocity of 5 feet per second. How much time does the diver have
to perform acrobatic maneuvers before hitting the water?
WEB DEVELOPER
Source: World High Diving Federation
Web developers use
hypertext markup language
W
W
W
A Web developer
76.
ORLD
IDE
EB
Click on
x
(HTML) to create electronic
one of the
is creating a Web site devoted to mountain
buttons
below to go
pages for the World Wide
x
to different
parts of
Welcome to The Climber Forums!
climbing. Each page on the Web site will have
our site.
This section is devoted to the discussion of all
Web. A Web browser
CTS
aspects of climbing. We have created several
NEWS
topic folders below where you may share your
frames along its top and left sides showing the
FORUMS
7 in.
experiences. Be sure to check out our live chat!
translates HTML into pages
PHOTOS
Climbing
Clubs
name of the site and links to different parts of
that can be viewed on a
MAPS
Hiking
Nature/Environment
WEATHER
the site. These frames will take up one third of
computer screen.
Skiing
Cooking on the Trail
FORUMS
Mountain Safety
Gear Reviews
the computer screen. What will the width x of
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CAREER LINK
Travel
Buy/Sell Equipment
the frames be on the screen shown?
11 in.
296
Chapter 5 Quadratic Functions
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