Intermediate Algebra (11th edition)

Step 3 Write an equation.The area of a parallelogram is given by where

bis the length of the longer side and his the distance between the longer

sides. Here, and

Let

Step 4 Solve. Distributive property

Standard form

Factor.

or Zero-factor property

or Solve each equation.

Step 5 State the answer.A distance cannot be negative, so reject as an

answer.The only possible answer is 4, so the distance between the longer

sides is 4 m. The length of the longer sides is

Step 6 Check.The length of the longer sides is 8 m more than the distance between

them, and the area is as required, so the answer checks.

NOW TRY

4 # 12 =48 m^2 ,

4 + 8 =12 m.

 12

x=- 12 x= 4

x+ 12 = 0 x - 4 = 0

1 x+ 1221 x- 42 = 0

x^2 + 8 x- 48 = 0

48 = x^2 + 8 x

48 = 1 x+ 82 x a=48,b=x+8,h=x.

a =bh

b= x+ 8 h=x.

a= bh,

348 CHAPTER 6 Factoring

NOW TRY
EXERCISE 7
The height of a triangle is 1 ft
less than twice the length of
the base. The area is 14
What are the measures of the
base and the height?

ft^2.

NOW TRY ANSWERS

7. base: 4 ft; height: 7 ft

CAUTION When applications lead to quadratic equations, a solution of the

equation may not satisfy the physical requirements of the problem, as in Example 7.

Reject such solutions as answers.

A function defined by a quadratic polynomial is called a quadratic function.(See

Chapter 9.) The next example uses such a function.

NOW TRY
EXERCISE 8
Refer to Example 8.After
how many seconds will the
rocket be 192 ft above the
ground?

8. 2 sec and 6 sec

Using a Quadratic Function in an Application

Quadratic functions are used to describe the height a falling

object or a projected object reaches in a specific time. For

example, if a small rocket is launched vertically upward

from ground level with an initial velocity of 128 ft per sec,

then its height in feet after tseconds is a function defined by

if air resistance is neglected. After how many seconds will

the rocket be 220 ft above the ground?

We must let and solve for t.

Let

Standard form

Divide by 4.

Factor.

or Zero-factor property

or Solve each equation.

The rocket will reach a height of 220 ft twice: on its way up at 2.5 sec and again on

its way down at 5.5 sec. NOW TRY

t= 2.5 t=5.5

2 t- 5 = 0 2 t- 11 = 0

12 t- 5212 t- 112 = 0

4 t^2 - 32 t+ 55 = 0

16 t^2 - 128 t+ 220 = 0

220 =- 16 t^2 + 128 t h 1 t 2 =220.

h 1 t 2 = 220

h 1 t 2 =- 16 t^2 + 128 t

EXAMPLE 8