Solve Quadratic Equations By The Quadratic Formula Worksheet - Chapter 10.6 Page 2
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1
2
3
4
5
6
7E
2
Solve a quadratic equation
X A M P L E
2
2 7 5 x.
Solve 2x
2
2 7 5 x
2x
Write original equation.
2
2 x 2 7 5 0
2x
Write in standard form.
}
Ï
2
2b 6
2 4ac
b
x 5
}}
Quadratic formula
2a
}}
Ï
2(21) 6
2
2 4(2)(27)
Substitute values in the quadratic
(21)
5
}}}
formula: a 5 2, b 5 21, and c 5 27.
2(2)
}
1 6 Ï
57
5
}
Simplify.
4
}
}
1 1 Ï
1 2 Ï
57
57
c
ø 2.14 and
ø 21.64.
The solutions are
}
}
4
4
at
CHECK
Write the equation in standard
2
2 x 2 7 5 0. Then graph
form, 2x
21.6
2.1
the related function y 5 2x
2
2 x 2 7.
The x-intercepts are about 21.6 and 2.1.
So, each solution checks.
✓
G
P
for Examples 1 and 2
UIDED
RACTICE
Use the quadratic formula to solve the equation. Round your solutions to
the nearest hundredth, if necessary.
2
2 8x 1 16 5 0
2
2 5n 5 21
2
5 7z 1 2
x
3n
4z
1.
2.
3.
E
3
Use the quadratic formula
X A M P L E
FILM PRODUCTION
For the period 197122001, the number y of films produced
2
in the world can be modeled by the function y 5 10x
2 94x 1 3900 where x is
the number of years since 1971. In what year were 4200 films produced?
Solution
2
y 5 10x
2 94x 1 3900
Write function.
4200 5 10x
2
2 94x 1 3900
Substitute 4200 for y.
0 5 10x
2
2 94x 2 300
Write in standard form.
}}
Substitute values in the quadratic
Ï
2(294) 6
2
2 4(10)(2300)
(294)
x 5
}}}
formula: a 5 10, b 5 294, and c 5 2300.
2(10)
INTERPRET
}
SOLUTIONS
94 6
Ï
20,836
5
}}
Simplify.
The solution 23 can
20
be ignored because
}
}
94 1
Ï
94 2
Ï
20,836
20,836
ø 12 and
ø 23.
23 represents the year
The solutions of the equation are
}}
}}
20
20
1968, which is not in
c
the given time period.
There were 4200 films produced about 12 years after 1971, or in 1983.
672
Chapter 10 Quadratic Equations and Functions
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