39.After experimentation, two physics students from Ameri-
can River College find that when a bottle of California
wine is shaken several times, held upright, and uncorked,
its cork travels according to the function defined by
where sis its height in feet above the ground tseconds
after being released. After how many seconds will it reach
its maximum height? What is the maximum height?
40.Professor Barbu has found that the number of students attending his intermediate algebra
class is approximated by
where xis the number of hours that the Campus Center is open daily. Find the number of
hours that the center should be open so that the number of students attending class is a
maximum. What is this maximum number of students?
41.Klaus Loewy has a taco stand. He has found that his daily costs are approximated by
where is the cost, in dollars, to sell xunits of tacos. Find the number of units of tacos
he should sell to minimize his costs. What is the minimum cost?
42.Mohammad Asghar has a frozen yogurt cart. His daily costs are approximated by
where is the cost, in dollars, to sell xunits of frozen yogurt. Find the number of units
of frozen yogurt he must sell to minimize his costs. What is the minimum cost?
43.The total receipts from individual income taxes by the U.S. Treasury in the years
2000 –2007 can be modeled by the quadratic function defined by
where represents 2000, represents 2001, and so on, and is in billions of
dollars. (Source: World Almanac and Book of Facts.)
(a)Since the coefficient of given in the model is positive, the graph of this quadratic
function is a parabola that opens up. Will the y-value of the vertex of this graph be a
maximum or minimum?
(b) In what year during this period were total receipts from individual taxes a minimum?
(Round down for the year.) Use the actual x-value of the vertex, to the nearest tenth,
to find this amount.
44.The percent of births in the United States to teenage mothers in the years 1990 –2005 can
be modeled by the quadratic function defined by
where represents 1990, represents 1991, and so on. (Source:U.S. National
Center for Health Statistics.)
(a)Since the coefficient of in the model is negative, the graph of this quadratic func-
tion is a parabola that opens down. Will the y-value of the vertex of this graph be a
maximum or a minimum?
(b) In what year during this period was the percent of births in the U.S. to teenage moth-
ers a maximum? (Round down for the year.) Use the actual x-value of the vertex, to
the nearest tenth, to find this percent.
45.The graph on the next page shows how Social Security trust fund assets are expected to
change, and suggests that a quadratic function would be a good fit to the data. The data
are approximated by the function defined by
ƒ 1 x 2 =-20.57x^2 +758.9x-3140.
x^2
x= 0 x= 1
ƒ 1 x 2 =-0.0198x^2 +0.1054x+12.87,
x^2
x= 0 x= 1 ƒ 1 x 2
ƒ 1 x 2 =22.88x^2 - 141.3x+1044,
C 1 x 2
C 1 x 2 =x^2 - 70 x+1500,
C 1 x 2
C 1 x 2 =x^2 - 40 x+610,
S 1 x 2 =-x^2 + 20 x+80,
s 1 t 2 =- 16 t^2 + 64 t+1,
550 CHAPTER 9 Quadratic Equations, Inequalities, and Functions
