4.5: Do Now: Review 4.5: Do Now: Review 4.3/4.4.4.3/4.4.

The area of a rectangle with length = 3x + 1and width = 2x + 1 is 22. Write and solve anequation to find the dimension of the rectangle.

Algebra IIAlgebra IIAlgebra IIAlgebra II4.5: Solve quadratic equations by 4.5: Solve quadratic equations by

finding the square root.finding the square root.

HW: p.269 (4-14 even), p.1013 (29-31 HW: p.269 (4-14 even), p.1013 (29-31 all)all)

Quiz 4.5, 4.7 (and word problems): Quiz 4.5, 4.7 (and word problems): Tuesday, Oct. 28Tuesday, Oct. 28thth

Simplify.Simplify.

156)2

24)1

Product and Product and Quotient PropertyQuotient Property

• Product Property

• Quotient Property

yxxy

y

x

y

x

Simplify.Simplify.150)3

25

11)4

Extra Practice: Simplify.Extra Practice: Simplify.

64

9)6

103245)5

Rationalizing the Rationalizing the DenominatorDenominator

• Can never have a radical in the denominator of a fraction.

You must rationalize the denominator.

2

7

2

2

Examples of Rationalizing Examples of Rationalizing the Denominatorthe Denominator

3

25)1 22

18)2

ConjugatesConjugates• The conjugate of • We can use conjugates to simplify

expressions (by rationalizing the denominator) like:

•Multiply the numerator and denominator by the conjugate of the denominator.

73 is 73

73

2

73

73

Simplify:Simplify:

206

4)1

62

35)2

4.5: Do Now: Review 4.3/4.44.5: Do Now: Review 4.3/4.4Friday’s Friday’s HW: p.269 (4-14 even), p.1013 HW: p.269 (4-14 even), p.1013

(29-31)(29-31)The product of two consecutive numbers is210. Write and solve an equation to find thetwo numbers.

Algebra IIAlgebra IIAlgebra IIAlgebra II4.5: Solve quadratic equations by 4.5: Solve quadratic equations by

finding the square root.finding the square root.

HW: p.269-270 (14-34 even)HW: p.269-270 (14-34 even)

Quiz 4.5, 4.7 (and word problems): Quiz 4.5, 4.7 (and word problems): Wednesday, Oct. 29Wednesday, Oct. 29thth

Solving Quadratic Solving Quadratic EquationsEquations

Solve:(Take square root of both sides)

8

64

x

x

642 x

Solving Quadratic Solving Quadratic EquationsEquations

Solve:1.) 2.) 644 2 x 8

3

1 2 x

Solving Quadratic Solving Quadratic EquationsEquations

Solve:3.)

4.)

8152 2 x

1312)8( 2 x

Solving Quadratic Solving Quadratic EquationsEquations

Solve:5.) 437)3(2 2 x

Solving Quadratic Solving Quadratic EquationsEquations

Solve:6.) 526)3(

2

1 2 x