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10.6

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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Parent category: Education