Intermediate Algebra (11th edition)

In the model, represents 2010,

represents 2015, and so on, and

is in billions of dollars.

(a)Concept Check How could you have

predicted this quadratic model would

have a negative coefficient for based

only on the graph shown?

(b)Algebraically determine the vertex of

the graph, with coordinates to four sig-

nificant digits.

(c)Interpret the answer to part (b) as it

applies to this application.

x^2 ,

ƒ 1 x 2

x= 15

x= 10

SECTION 9.6 More About Parabolas and Their Applications 551

4000

3000

2000

1000

0

2010 2015 2020 2025 2030

Billions of Dollars

Year

*Projected

Social Security Assets*

Source: Social Security Administration.

46.The graph shows the performance of
investment portfolios with different
mixtures of U.S. and foreign invest-
ments over a 25-yr period.
(a)Is this the graph of a function?
Explain.
(b)What investment mixture shown
on the graph appears to represent
the vertex? What relative amount
of risk does this point represent?
What return on investment does it
provide?
(c)Which point on the graph repre-
sents the riskiest investment mix-
ture? What return on investment
does it provide?

47.A charter flight charges a fare of $200 per person, plus $4 per person for each unsold seat
on the plane. If the plane holds 100 passengers and if xrepresents the number of unsold
seats, find the following.
(a)A function defined by that describes the total revenue received for the flight
(Hint:Multiply the number of people flying, , by the price per ticket, .)
(b) The graph of the function from part (a)
(c) The number of unsold seats that will produce the maximum revenue
(d) The maximum revenue

48.For a trip to a resort, a charter bus company charges a fare of $48 per person, plus
$2 per person for each unsold seat on the bus. If the bus has 42 seats and xrepresents the
number of unsold seats, find the following.
(a)A function defined by that describes the total revenue from the trip (Hint:
Multiply the total number riding, , by the price per ticket, .)
(b)The graph of the function from part (a)
(c)The number of unsold seats that produces the maximum revenue
(d)The maximum revenue

Graph each interval on a number line. See Section 2.5.

Solve each inequality. See Section 2.5.

52. 
    
    
    
    53. 54.-
    
    
    
    

1

2

3 - x... 5 - 2 x+ 164 x- 375

3 1, 5 4 1 - 6, 1 4 1 - q, 1 4 ́ 3 5, q 2

PREVIEW EXERCISES

42 - x 48 + 2 x

R 1 x 2

100 - x 200 + 4 x

R 1 x 2

LOOKING FOR THE RIGHT MIX

A portfolio that includes international investments

potentially can produce higher returns with lower

risk than a 100% U.S. stock portfolio.

Average Annual Total Return

Source: Financial Ink Newsletter, Investment Management and

Research, Inc. Thanks to David Van Geffen for this information.

Lower Higher

(standard deviation of annual total returns)

Risk

13.50%

14.00%

14.50%

15.00%

15.50%

16.00%

14% 16% 18% 20% 22% 24%

100%

Foreign

Stocks

(EAFE)

20%/80%

40%U.S/60%

Foreign Stocks

60%/40%

80%/20%

100%U.S. (S&P 500)