solving quadratics with square roots

4.54.5Solving Quadratic Equations Solving Quadratic Equations

by Finding Square Rootsby Finding Square Roots

(p. 250-253)(p. 250-253)

How would you solve the equation:How would you solve the equation:xx22 = 4 = 4

(take the square root of each side!)(take the square root of each side!)

* Remember, the square root of a positive # has 2 answers! (one + and one -)

*2- 2

4

4

2

2

orx

x

x

RadicalRadical

3Radical Radical

signsignRadicandRadicand

Properties of Square RootsProperties of Square Roots

(a>0 and b>0)

1. Product Property –

2. Quotient Property-

baab *

Example:Example:

10210*410*440

b

a

b

a

Example:Example:

2

3

4

3

4

3

ExamplesExamples

1.

2.

3.

500 5*100 5*100 510

6*123 6*123 723 2*363

26*3 218

9

25

9

25

3

5

Rationalizing the DenominatorRationalizing the Denominator

You CANNOT leave a radical in the denominator of a fraction!

(the numerator is OK)

Just multiply the top & bottom of the fraction by the radical to “rationalize” the

denominator.

More Examples!More Examples!

1.

2.

3

25

3

25

3

5

3*

3*

9

35

3

35

Can’t have a tent in the Can’t have a tent in the basement!basement!

11

2

11

2

11*

11*

121

22

11

22

Solving Quadratic EquationsSolving Quadratic Equations1. Solve. 3 - 5x2 = -9

-3 -3

-5x2 = -12

-5 -5

x2 = 5

12

5

122 x

5

152

5

15*4

25

60

5*5

5*12

5

12 x

2.Solve. 3(x-2)2=21 3 3

(x-2)2 = 7

7)2( 2 x

72 x

72 x

More Examples!More Examples!

3. Solve. 4x2-6=42

+6 +6

4x2=48

4 4

x2 = 12

122 x

323*4 x

4. Solve. 4. Solve. 6)4(5

1 2 x

30)4( 2 x

30)4( 2 x

304 x

304 x

Falling Objects!Falling Objects!

• Use h = -16t2 + h0

Height Height of the of the object object after it after it

has has fallenfallen

# of seconds # of seconds after the after the object is object is droppeddropped

Object’s Object’s initial initial heightheight

ExampleExample• The tallest building in

the USA is in Chicago, Illinois. It is 1450 ft. tall. How long would it take a penny to drop from the top of the building to the ground?

1450160 2 t

0216 hth

2161450 t2625.90 t

2625.90 t

seconds 52.9t