Intermediate Algebra (11th edition)

If the Leaning Tower is about 180 ft tall, use Galileo’s

formula to determine how long it would take an object

dropped from the top of the tower to fall to the ground.

(Source: http://www.brittanica.com)

Galileo’s formula

Let.

Divide by 16.

or Square root

property

Time cannot be negative, so we discard the negative solution. Using a calculator,

so The object would fall to the ground in about 3.4 sec.

NOW TRY

OBJECTIVE 3 Solve quadratic equations of the form by

extending the square root property. We can solve more complicated equations

by extending the square root property.

Extending the Square Root Property

Solve

Substitute for and 36 for

kin the square root property.

or

or Simplify square roots.

or Add 5.

CHECK Original equation

Let Let

✓True ✓True

Both solutions satisfy the original equation. The solution set is 5 - 1, 11 6.

36 = 36 36 = 36

62  36 1 - 622  36

111 - 522  36 x=11. 1 - 1 - 522  36 x=-1.

1 x- 522 = 36

x= 11 x= - 1

x- 5 = 6 x- 5 =- 6

x- 5 = 236 x- 5 = - 236

1 x- 522 x^2

1 x- 522 = 36

x^2 =^ k

1 x- 522 =36.

EXAMPLE 4

1 axb 22 c

2 11.25L3.4 tL3.4.

t= 2 11.25 t=- 2 11.25

11.25= t^2

180 = 16 t^2 d= 180

d= 16 t^2

498 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

NOW TRY
EXERCISE 3
Tim is dropping roofing nails
from the top of a roof 25 ft
high into a large bucket on the
ground. Use the formula in
Example 3to determine how
long it will take a nail
dropped from 25 ft to hit the
bottom of the bucket.

NOW TRY ANSWERS
3.1.25 sec 4. 5 - 8, 2 6

NOW TRY
EXERCISE 4
Solve 1 x+ 322 =25.

NOW TRY

Extending the Square Root Property

Solve

or Square root property

or Add 3.

or Divide by 2.

or x= 218 = 29 # 2 = 322

3 - 322

2

x=

3 + 322

2

x=

3 - 218

2

x=

3 + 218

2

2 x= 3 + 218 2 x= 3 - 218

2 x- 3 = 218 2 x- 3 = - 218

12 x- 322 = 18.

EXAMPLE 5

Galileo Galilei (1564 –1642)