5-35-3Solving Quadratic Equations by Solving Quadratic Equations by

finding Square Roots.finding Square Roots.

Objective: Solve quadratic functions by finding square roots.

Properties of Square Roots (a > 0, b > 0)

Product Property : ab a b

Quotient Property:a a

b b

A square root expression is considered simplified IF:

2. There is no radical in the denominator.

1. No radicand has a perfect square root factor other than 1

EXAMPLES: Simplify the expressions:

24 4 6 2 6

7

16

7 7 7

2 2 44 4

7

2

7 2 14

22 2

Example 1: Solve 22 1 17x

2

2

2 16

8

8

4 2

2 2

x

x

x

x

x

Example 2: Solving a Quadratic Equation

Solve: 215 7

3x

25 21

5 21

5 21

x

x

x

Homework:

Page 267: #19-47 EOO

BRING BOOKS TOMORROW

IN-CLASS TOMORROW:

P.267-268 #51- 67 ODD

Example 4When an object is dropped, its speed continually increases, and therefore its height above ground decreases at a faster and faster rate.The height h (in feet) of the object t seconds after it is dropped is modeled by the function

216 oh t h

Where ho is the initial height

The tallest building in the United States is in Chicago. It is 1450 feet talla) How long would it take a penny to drop from the top of this building?

0

2

Let h initial height = 1450 ft.

16 oh t h

2

2

2

2

0 16 1450

1450 16

1450

16

90.625

90.625

9.5

t

t

t

t

t

t

b) How fast would the penny be traveling when it hits the ground if the speed is given by s=32t where t is the number of seconds since the penny was dropped.

32s t 32 9.5

304 ft/sec.

s

s