2. Quadratic Equations, Inequalities, and Functions
Chapter 10
Quadratic Equations, Inequalities,
and Functions

3. The Square Root Property and Completing the Square
10.1
The Square Root Property
and Completing the Square

4. 10.1 The Square Root Property and Completing theSquare
Objectives
Review the zero-factor property.
Learn the square root property.
Solve quadratic equations of the form (ax + b)2 = c by using the square root property.
Solve quadratic equations by completing the square.
Solve quadratic equations with nonreal complex solutions.
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5. 10.1 The Square Root Property and Completing the Square
Quadratic Equations and the Zero-Factor Property
In Section 7.5, we defined a quadratic equation as follows:
Example:
We then used factoring and the zero-factor property to solve the equation
Solving:
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6. 10.1 The Square Root Property and Completing the Square
Not all quadratic equations are factorable over the integers. We will now examine other methods for solving quadratic equations regardless of whether they can be factored. We base these methods on the following property.
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7. 10.1 The Square Root Property and Completing the Square
Using the Square Root Property
Solve each equation.
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8. 10.1 The Square Root Property and Completing the Square
Using the Square Root Property
Each solution can be checked by substituting back into the original equation.
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9. 10.1 The Square Root Property and Completing the Square
Solving Quadratic Equations of the Form (ax + b)2 = c
Solve.
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10. 10.1 The Square Root Property and Completing the Square
Solving Quadratic Equations of the Form (ax + b)2 = c
Check.
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11. 10.1 The Square Root Property and Completing the Square
Solve Quadratic Equations by Completing the Square
We can use the observations of the previous cases to build our own perfect square trinomials and, in doing so, solve some quadratic equations.
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12. 10.1 The Square Root Property and Completing the Square
Solve Quadratic Equations by Completing the Square
Cont’d from previous
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13. 10.1 The Square Root Property and Completing the Square
Solve Quadratic Equations by Completing the Square
Solving:
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14. 10.1 The Square Root Property and Completing the Square
Solve Quadratic Equations by Completing the Square
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15. 10.1 The Square Root Property and Completing the Square
Completing the Square with a = 1
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16. 10.1 The Square Root Property and Completing the Square
Completing the Square with
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17. 10.1 The Square Root Property and Completing the Square
Quadratic Equations with Nonreal Complex Solutions
Solve each equation.
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18. 10.1 The Square Root Property and Completing the Square
Quadratic Equations with Nonreal Complex Solutions
Solve.
Copyright © 2010 Pearson Education, Inc. All rights reserved.