Solve Quadratic Equations By The Quadratic Formula Worksheet - Chapter 10.6
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2
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5
6
710.6
Solve Quadratic Equations
by the Quadratic Formula
You solved quadratic equations by completing the square.
Before
You will solve quadratic equations using the quadratic formula.
Now
So you can solve a problem about film production, as in Example 3.
Why?
2
1 bx 1 c 5 0, you
Key Vocabulary
By completing the square for the quadratic equation ax
can develop a formula that gives the solutions of any quadratic equation in
quadratic formula
•
standard form. This formula is called the quadratic formula. (The quadratic
formula is developed on page 727.)
For Your Notebook
KEY CONCEPT
The Quadratic Formula
2
1 bx 1 c 5 0 are
The solutions of the quadratic equation ax
Î
}
2b 6
2
2 4ac
b
x 5
where a Þ 0 and b
2
2 4ac ≥ 0.
}}
2a
★
E
1
Standardized Test Practice
X A M P L E
2
1 5x 5 8?
What are the solutions of 3x
8
8
8
8
A 21 and 2
B 21 and
C 1 and 2
D 1 and
}
}
}
}
3
3
3
3
ANOTHER WAY
Solution
Instead of solving the
equation, you can check
2
1 5x 5 8
3x
Write original equation.
the answer choices in
2
1 5x 2 8 5 0
3x
Write in standard form.
the equation.
}
Ï
2b
6
2
2
b
4ac
x 5
}}
Quadratic formula
2a
}}
Ï
25
6
2
2 4(3)(28)
Substitute values in the quadratic formula:
5
x 5
}}
5
5
5 2
3, b
5, and c
8.
2(3)
a
}
25 6 Ï
121
5
}
Simplify.
6
25 6 11
5
}
Simplify the square root.
6
25 1 11
25 2 11
8
5 1 and
5 2
}
The solutions of the equation are
}
}
.
3
6
6
c
A B C D
The correct answer is C.
671
10.6 Solve Quadratic Equations by the Quadratic Formula
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