Solve Quadratic Equations By The Quadratic Formula Worksheet - Chapter 10.6 Page 5
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7SOLVING QUADRATIC EQUATIONS
Solve the quadratic equation using any
method. Round your solutions to the nearest hundredth, if necessary.
22x
2
5 232
2
2 8x 5 216
2
1 2x 2 6 5 0
x
x
34.
35.
36.
2
5 12x 2 36
2
1 4x 5 9
24x
2
1 x 5 217
37.
x
38.
x
39.
2
2 1 5 6x
2
1 2
22x
2
1 5 5 3x
2
2 10x
(x 1 13)
2
5 25
11x
40.
41.
42.
GEOMETRY
Use the given area A of the rectangle to find the value of x.
Then give the dimensions of the rectangle.
A 5 91 m
2
A 5 209 ft
2
43.
44.
(x 1 2) m
(4x 2 5) ft
(2x 1 3) m
(4x 1 3) ft
2
1 bx 1 c 5 0 are
CHALLENGE
The solutions of the quadratic equation ax
45.
}
}
Ï
Ï
2
2b 1
2
2 4ac
2b 2
2 4ac
b
b
5
and x 5
}}
}}
. Find the mean of the solutions.
x
2a
2a
is the mean of the solutions related to the graph of y 5 ax
2
1 bx 1 c?
How
Explain.
P
S
ROBLEM
OLVING
ADVERTISING
EXAMPLE 3
46.
For the period 199022000, the amount of money y (in
billions of dollars) spent on advertising in the U.S. can be modeled by
on p. 672
the function y 5 0.93x
2
1 2.2x 1 130 where x is the number of years since
for Exs. 46–47
1990. In what year was 164 billion dollars spent on advertising?
CELL PHONES
For the period 198522001, the number y (in millions) of
47.
cell phone service subscribers in the U.S. can be modeled by the function
y 5 0.7x
2
2 4.3x 1 5.5 where x is the number of years since 1985. In what
year were there 16,000,000 cell phone service subscribers?
MULTI-STEP PROBLEM
A football is punted from a height of 2.5 feet above
48.
the ground and with an initial vertical velocity of 45 feet per second.
Not drawn to scale
5.5 ft
2.5 ft
Use the vertical motion model to write an equation that gives
a.
the height h (in feet) of the football as a function of the time t (in
seconds) after it has been punted.
b.
The football is caught 5.5 feet above the ground as shown in the
diagram. Find the amount of time that the football is in the air.
675
10.6 Solve Quadratic Equations by the Quadratic Formula
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