Algebra 2

5.3 – Solving Quadratics by Square Roots

Graph the quadratic equation.

Warm-Up

21( 3) 42

y x

Vertex: (-3, 4)Axis of symmetry: x = -3

Simplify radical expressionsRationalize the denominatorSolve quadratic equations

Objectives:

Product Property:

Quotient Property:

Square Root Properties

a b ab

a a

b b

1. No fractions in square roots

2. No perfect squares in the radical

3. No radicals in the denominator

The NO-NO’s of Square Roots

Did you know…?That it is against the law in 32 states (including Illinois)

to leave a radical in the denominator of a fraction.

Steps:1. Use a “factor

tree” to factor completely

2. Circle pairs of the same number (they go out)

3. Any other factors not part of a pair stay in

Product Property

500

100 5

10 10

2 5 52

2 5 5 10 5

Steps:1. Use a “factor tree” to

factor completely2. Circle pairs of the same

number (they go out)3. Any other factors not

part of a pair stay in

Product Property

1)

2)

3)

3 12 6

3 12

15 6 3 10

18 2

6

Steps:1. Split up into two

square root problems

2. Simplify the numerator and denominator

3. Remember the “NO-NO” rules

Quotient Property

64

9

64

9

8

3

Steps:1. Split up into two

square root problems

2. Simplify the numerator and denominator

3. Remember the “NO-NO” rules

Quotient Property25

3

25

3

25 3

3 3

5 3

3

Steps:1. Split up into two

square root problems

2. Simplify the numerator and denominator

3. Remember the “NO-NO” rules

Quotient Property

1)

2)

2

1122

11

18

362

2

Steps:1. Isolate the variable2. Include both answers

Solving a Quadratic Equation

1)

2)

22 1 17x 2 2x

21( 5) 73x 5 21x

Note: This method only works when there is no “b” term!

Steps:1. Isolate the variable2. Include both answers

Solving a Quadratic Equation

3)

4)

23 108x 6x

2

6 48

x 4 5x

pg. 267 #32-34, 38, 41, 49, 54-57, 60

Quiz on Tuesday, November 20th

Homework/Reminders: