Section 9.1The Square Root Property

Section 9.2The Quadratic Formula

Overview

• Recall that a quadratic equation is in the form

• Up to this point, we have solved quadratic equations by factoring…

02 cbxax

09

0532

0158

2

2

2

x

xx

xx

The Problem?

• Although every quadratic equation has at least one solution, not every quadratic equation will factor…

010

0432

0178

2

2

2

x

xx

xx

The Square Root Property

• The big idea: Given (something)2 = a number:1.Take the square root of both sides (the square

root and the squared exponent will cancel each other out, leaving just the radicand.

2.Don’t forget the “plus or minus”3.Simplify the radical4.Isolate the variable

Examples

496

02005

54

225

2

2

2

2

x

z

x

x

2774

96

18

1052

2

2

2

2

m

t

x

x

The Quadratic Formula

• Can be used on any quadratic equation (even the ones that will factor).

a

acbbx

2

42

Steps In The Process

1. Make sure your equation is in the right form.2. Identify a, b, and c. Substitute them into the

formula.3. Watch your signs!4. When you square a negative, you get a positive.

I don’t care what your calculator says.5. Simplify the radical.6. Be careful when you reduce (all three places, all

by the same factor, or not at all).

Examples

232

625

6

1

3

0283

2

2

zz

xx

pp

xx

Summary of Solving Quadratic Equations

• If you can factor it, factor it. Then set each factor equal to zero.

• If you can’t factor it, or if it won’t factor, use the quadratic formula.

• If it comes to you in the form (something)2 = a numberdo not unravel it. Use the square root property.