The Square Root Property and Completing the Square

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 07:22 PM UTC

OBJECTIVE:
1. Review the zero-factor property.
2. Learn the square root property.
3. Solve quadratic equations of the form (ax + b)^2 = c by using the square root property.
4. Solve quadratic equations by completing the square.
5. Solve quadratic equations with nonreal complex solutions.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 10.1 - 1

2. Chapter 10
Quadratic Equations,
Inequalities,
and Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 10.1 - 2

3. 10.1
The Square Root Property
and Completing the Square
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 10.1 - 3

4. 10.1 The Square Root Property and Completing theSquare
Objectives
1. Review the zero-factor property.
2. Learn the square root property.
3. Solve quadratic equations of the form
(ax + b)2 = c by using the square root
property.
4. Solve quadratic equations by completing the
square.
5. Solve quadratic equations with nonreal
complex solutions.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 4

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:
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 5

6. 10.1 The Square Root Property and Completing the Square
The Square Root Property
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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 6

7. 10.1 The Square Root Property and Completing the Square
Using the Square Root Property
Solve each equation.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 7

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 8

9. 10.1 The Square Root Property and Completing the Square
Solving Quadratic Equations of the Form (ax + b)2 = c
Solve.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 9

10. 10.1 The Square Root Property and Completing the Square
Solving Quadratic Equations of the Form (ax + b)2 = c
Check.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 10

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 11

12. 10.1 The Square Root Property and Completing the Square
Solve Quadratic Equations by Completing the Square
Cont’d from previous
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 12

17. 10.1 The Square Root Property and Completing the Square
Quadratic Equations with Nonreal Complex Solutions
Solve each equation.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 17

Book a Trial Class

Download