MATH085 In-Class Assignment
Contents
6.1 Adding and subtracting polynomials ......................................................................................................... 2
6.2 Multiply polynomials ........................................................................................................................................ 2
6.3 Special Products ................................................................................................................................................ 3
6.4 Polynomials in several variables ................................................................................................................. 4
6.5 Dividing Polynomials ....................................................................................................................................... 4
6.6 Dividing Polynomials by Binomials ............................................................................................................ 5
6.7 Negative exponents and scientific notations ......................................................................................... 5
7.1 Greatest Common Factor & Factoring by Grouping ............................................................................ 6
7.2 Factoring trinomials whose leading coefficient is one ........................................................................ 6
7.3 Factoring trinomials whose leading coefficient is not one ................................................................ 6
7.4 Factoring special forms .................................................................................................................................. 7
7.5 A General Factoring Strategy ...................................................................................................................... 7
7.6 Solving Quadratic Equations by Factoring .............................................................................................. 7
8.1 Rational expressions and their simplification ........................................................................................ 8
8.2 Multiplying and Dividing Rational Expressions ...................................................................................... 8
8.3 Adding and Subtracting Rational Expressions with Same Denominator ..................................... 9
8.4 Adding and subtracting rational expressions with different denominators................................ 9
9.1 Finding Roots ................................................................................................................................................... 10
9.2 Multiplying and Dividing Radicals ............................................................................................................. 10
9.3 Operations with Radicals ............................................................................................................................. 11
9.4 Rationalize the Denominator...................................................................................................................... 11
9.5 Radical Equations ........................................................................................................................................... 12
9.6 Rational Exponents ........................................................................................................................................ 12
10.1a Solving Quadratic Equations using Square Root Property......................................................... 13
10.1b Solving Quadratic Equations using Square Root Property ........................................................ 13
10.2 Solving Quadratic Equations by Completing the Square .............................................................. 13
10.3a Quadratic Formula ..................................................................................................................................... 14
10.5 Graphs of Quadratic Equations ............................................................................................................... 14
Page 1
MATH085 In-Class Assignment
6.1 Adding and subtracting polynomials
Group 1: The common cold is caused by a rhinovirus. The polynomial  0.75 x 4  3x 3  5 describes the
billions of viral particles in our bodies after x days of invasion. Find the number of viral particles, in
billions, after 0 days (the time of the cold’s onset when we are still feeling well), 1 day, 2 days, 3 days,
and 4 days. After how many days is the number of viral particles at a maximum and consequently we feel
the sickest? By when should we feel completely better?
Group 2 & 3: (p.348, #103) Use the graph and the polynomials on page 348.
Group 2 use the second degree polynomials and Group 3 use the third degree polynomials to answer the
following questions:
a. Use the equations to find a model for M – W.
b. According to the model you found in part (a), what is the difference in median annual income
between men and women with 14 years of education?
c. According to the data displayed by the graph on page 348, what is the actual difference between
men and women with 14 years of education? Did the model in part (b) over or under estimate this
difference? By how much?
Compare your results with the other group. Which model do you think is a better fit for the actual data?
6.2 Multiply polynomials
Groups 1 & 2 (p.359 #103 & 104) (a) Express the area of the large rectangle as the product of the two
binomials. (b) Find the sum of the areas of the four smaller rectangles. (c) Use polynomial multiplication
to show that your expressions for area in parts (a) and (b) are equal.
Group 1
2x
Group 2
1
2x
x
x
2
2
3
Group 3 (p.359, #121) Find a polynomial that represents the area of the shaded region.
x+4
X
x
x+4
Page 2
MATH085 In-Class Assignment
6.3 Special Products
Group 1: (p.366 #97 & 98) The square garden shown on page 366 measures x yards on each
side. The garden is to be expanded so that one side is increased by 2 yards and an adjacent
side is increased by one yard.
a. Draw a picture of the original garden with the expanded sections. Label the length and
width of the expanded garden.
b. Write a product of two binomials that expresses the area of the larger garden (with units
labeled).
c. Write a polynomial in standard form that expresses the area of the larger garden.
Group 2: (p.367 #101 & 102) The square painting in the figure on page 366 measures x inches
on each side. The painting is uniformly surrounded by a 1-inch wide frame.
a. Write a polynomial in standard form that expresses the area of the square that includes the
painting and the frame.
b. Write an algebraic expression that describes the area of the frame.
Group 3: (p.367 #118) Express the area of the plane figure shown as a polynomial in standard
form.
x
x
x-1
x+3
Page 3
MATH085 In-Class Assignment
6.4 Polynomials in several variables
Group 1 (p.374 #88) The storage shed shown on p.374 has a volume given by
2 x 2 y  0.5x 2 y .
A small business is considering the shed installed. The shed’s height, 2x,
is 26 feet and its length, y, is 27 feet. Find the volume of the storage shed. If the business
requires at least 18,000 cu. ft. of storage space, should they construct this shed?
Group 2 (p.356 #89-91) An object that is falling or vertically projected into the air has its
height, in feet, above the ground given by
h  16t 2  v0t  h0
where h is the height, in
feet, vo is the original velocity of the object, in feet per second, t is the time the object is in
motion, in seconds, and ho is the height, in feet, from which the object is dropped or projected.
The figure, on p. 374, shows that a ball is thrown straight up from a rooftop at an original
velocity of 80 feet/second from a height of 96 feet. The ball misses the rooftop on its way down
and eventually strikes the ground. How high above the ground will the ball be 2, 4 and 6
seconds after being thrown?
Group 3 (p.375 #109) Find a simplified polynomial in two
variables that describes the area of the shaded region.
x+8y
x
x
x
x
x+10y
6.5 Dividing Polynomials
Group 1 (p.384 #87) Polynomial models for the U.S. film box office receipts in millions of
dollars, R
 3.6 x 2  158 x  2790 , and admissions in millions of tickets sold,
A  0.2 x 2  21x  1015 . (a) Use the data from the bar graphs on the bottom of p. 383 to
determine the average admission price for a film ticket in the year 2000. (b) Use the models to
write an algebraic formula that represents the average admission fee for a film ticket x years
after 1980. (c) Use the formula from part (b) to determine the average ticket price for the year
2000. Does it over or under estimate the actual you determined in part (a)?
Group 2 (p.383 #83) Divide the sum of  y  52 and
 y  5 y  5 by 2 y .
 9 x 3  6 x 2   12 x 2 y 2  4 xy2 
  

3x
2 xy2

 

Group 3 (p.383 # 82) Simplify the expression 

Page 4
MATH085 In-Class Assignment
6.6 Dividing Polynomials by Binomials
Groups 1 (p.392 #47) You just signed a contract for a new job. The salary for the first year is
$30,000 and there is to be a percent increase in your salary each year. The expression
30,000 x n  30,000
x 1
describes your salary over n years, where x is the
sum of 1 and the yearly percent increase, expressed as a decimal.
(a) Use the given quotient of polynomials to represent your total salary over three years, and
then (b) simplify that expression by performing the division. (c) Suppose you are to receive an
increase of 5% per year. (x = 1 + 0.05). Substitute 1.05 into the expression for x in both
expressions, from part (a) and part (b). What is your total salary over the three years?
Group 2: (p.391#35) Divide as indicated the check your answer by showing that the product of
the divisor and quotient , plus the remainder, is the dividend:
y4  2y2  5
y 1
Group 3 (p.372 #45) Draw a picture to help you solve this problem. Write a simplified
polynomial that represents the length of the rectangle when its area is
inches and its width is
x 3  3x 2  5 x  3 square
x  1 inches.
6.7 Negative exponents and scientific notations
Group #1 (p.405 #149) In 2007, the U.S. population was approximately 3.1 x 108 and each
person spent about $120 per year on ice cream, express the total annual spending on ice cream
in scientific notation. (Make sure to use the appropriate number of significant digits.)
Group #2 (p.404 #147) (a) In 2005, the U.S. government collected$2.27 trillion in taxes.
Express this number in scientific notation. (b) In 2005, the U.S. population was about 298
million. Express this in scientific notation. (c) Using parts (a) and (b), if this was divided evenly
among all Americans, how much would each citizen pay? (Make sure to use the appropriate
number of significant digits.)
Group #3 (p.405 #151) Use the motion formula d = rt, distance equals rate times time, and
the fact that light travels at the rate of 1.86 x 105 miles per second. If the moon is
approximately 2.325 x 105 miles from Earth, how many seconds does it take moonlight to reach
Earth? (Make sure to use the appropriate number of significant digits.)
Page 5
MATH085 In-Class Assignment
Chapter 7
7.1 Greatest Common Factor & Factoring by Grouping
GROUP 1: (p.420 #66) Factor by Grouping, show your steps
x 3  3x 2  4 x  12
Group 2: (p.420 #88) Write a polynomial that represents the shaded area in the figure shown
on page 420 #88. Then factor the polynomial. The square is 4x on each side.
Group 3: (p.420 #89) An explosion causes debris to rise vertically with an initial velocity of 64
feet per second. The polynomial 64 x  16 x 2 describes the height of the debris above the ground,
in feet, after x seconds. (a) Find the height of the debris after 3 seconds. (b) Factor the
polynomial. (c) Use the factored form of the polynomial to find the height after 3 seconds. Do
you get the same answer as you did for part (a)? If so, does this prove that your factorization is
correct? Explain.
7.2 Factoring trinomials whose leading coefficient is one
Groups 1 & 2: (a) Factor the polynomial completely. (b) Evaluate both the original and its
factored form for t = 2. Do you get the same answer? Describe what the answer means in the
context of the problem.
Group 1 (p.428 #77) You dive directly upward from a board that is 32 feet high. After t
seconds, your height above the water is described by:  16t 2  16t  32 . (c) What does each of
the terms in the original equation represent in the context of the problem? (The book does not
talk about this—make an educated guess)
Group 2 (p.429 #78) You dive directly upward from a board that is 48 feet high. After t
seconds, your height above the water is described by:  16t  32t  48 . (c) Use the equation to
determine the highest point you reached in your dive. (The book does not talk about this—
sketch what you think the path of your dive looks like, and then explain how you found the
highest point.)
2
Group 3 (p.429 #96) A box with no top is to be made from an 8-inch by 6-inch piece of metal
by cutting identical squares from each corner and turning up the sides. The volume of the box is
modeled by: 4 x  28 x  48 x . Factor the polynomial completely. Then use the dimensions
given on the box on page 429 and show that its volume is equivalent to the factorization that
you obtained.
3
2
7.3 Factoring trinomials whose leading coefficient is not one
Group 1 (p.436 # 88) Factor completely 6 y  1x 2  33 y  1x  15 y  1
Group 2 (p.436 #84) Factor completely
6 x 2 y  2 xy  60 y
Group 3 (p.436 #92) (a) Factor 2 x 2  5 x  3 (b) Use the factorization method you used from
part (a) to help you to factor 2 y  1  5 y  1  3 and then simplify each factor.
2
Page 6
MATH085 In-Class Assignment
7.4 Factoring special forms
Find the formula for the area of the shaded region and express it in factored form.
GROUP 1 (p.445 # 102)
3
3
3
GROUP 2 (p.445 #100)
2
x
3x
2
3
x
GROUP 3 (p.445 #96) Factor completely
a
b
x  2
2
 49
3x
7.5 A General Factoring Strategy
GROUP 1 (p.453 #109) (The arrows originate
at the center of each of these concentric
circles.) Express the area of the shaded ring
shown in the figure in terms of π. Then factor
this expression completely.
x
GROUP 2 (p.453 #108) A building has a height
represented by x feet. The building’s base is a
square and its volume is x 3  60 x 2  900 x cubic
feet. Express the building’s dimensions in terms of x.
GROUP 3 (p.453 #107) A rock is dropped from the top of a 256-foot cliff. The height, in feet, of
the rock above the water after t seconds is modeled by the polynomial
expression completely.
256  16t 2 . Factor this
7.6 Solving Quadratic Equations by Factoring
GROUP 1 (p.463 #70&71) An explosion causes debris to rise vertically with an initial velocity of
2
72 feet per second. The formula h  16t  72t describes the height of the debris above the
ground, h feet, t seconds after the explosion. (a) How long will it take for the debris to hit the
ground? (b) When will the debris be 32 feet above the ground?
GROUP 2 (p.464 #72&73) The formula S  2 x 2  12 x  82 models spending by international
travelers to the U.S., S, in billions of dollars, x years after 2000. (a) In which years did
international travelers spend $72 billion? (b) In which years did international travelers spend
$66 billion?
GROUP 3 (p.465 #86) A vacant rectangular lot is being turned into a community vegetable
garden measuring 15 meters by 12 meters. A path of uniform width is to surround the garden. If
the area of the lot is 378 square meters, find the width of the path surrounding the garden.
(Draw a diagram to help you solve this problem.)
Page 7
MATH085 In-Class Assignment
Chapter 8
8.1 Rational expressions and their simplification
GROUP 1 (p.482 #86) The rational expression 60,000 x describes the cost, in dollars, to remove
100  x
x percent of the air pollutants in the smokestack emission of a utility company that burns coal to
generate electricity. (a) Evaluate the expression for x = 20, 50, and 80. Describe the meaning
of each evaluation in terms of percentage of pollutants removed and cost. (b) For what value of
x is the expression undefined? (c) What happens to the cost as x approaches 100%? How can
you interpret this observation?
GROUP 2 (p.482 #90) A company that manufactures small canoes has costs given by the
equation C 
20 x  20,000
in which x is the number of canoes made and C is the cost to make
x
each canoe. (a) Find the cost per canoe when making 100 canoes. (b) Find the cost per canoe
when making 10,000 canoes. (c) Does the cost per canoe increase or decrease as more canoes
are made? Explain why this happens.
GROUP 3 (p.483 #93) The mathematical model for calories needed per day, W, by women in
age group x to maintain a sedentary lifestyle is W  82 x 2  654 x  620 . The model for calories
needed per day, M, by men in age group x to maintain a sedentary lifestyle is
M  96 x 2  802 x  660 . (a) Determine the calories needed for women and for men between
the ages of 19 and 30 (age group 4). (b) Write a simplified expression for the ratio between the
calories needed by women as compared with men. (c) Write a simplified expression for the
difference in calories needed by women as compared to men.
8.2 Multiplying and Dividing Rational Expressions
GROUPs 1-3 Write a simplified rational expression for the area of the given figures. Assume all
measures are in inches.
GROUP 1 (p.490 #73) Rectangle with width of
x2  4
x 1
and length of 2
2
x  2x
x 1
GROUP 2 (p.490 #74) Rectangle with width of
x5
x6
and
length
of
x 2  36
x 2  7 x  10
GROUP 3 (p.490 # 75) Triangle with height of
18 x
x 1
and base of
2
3
x  3x  2
Page 8
MATH085 In-Class Assignment
8.3 Adding and Subtracting Rational Expressions with Same Denominator
GROUP 1 (p.498 #73) Anthropologists and forensic scientists classify skulls using
L  60W L  40W where L is the skull’s length and W is its width. (a)

L
L
Express the classification as a single rational expression. (2) If the value of the rational
expression in part (a) is less than 75, a
classified as long. A medium skull has
7
between 75 and 80, and a round skull
x4
value of over 80. Use your rational
expression from part (a) to classify a
4x  9
that is 5 inches wide and 6 inches long.
x4
GROUP 2 (p.498 #76) Find the
perimeter of the rectangle, which is measured in inches.
skull is
a value
has a
skull
GROUP 3 (p.498 #74) The temperature, in degrees Fahrenheit, of a dessert placed in a freezer
for t hours is modeled by
t  30
t  50
 2
t  4t  1 t  4t  1
2
(a) Express the temperature as a single rational expression. (b) Use your rational expression
from part (a) to find the temperature of the dessert, to the nearest hundredth of a degree, after
1 hour and after 2 hours.
8.4 Adding and subtracting rational expressions with different denominators
GROUP 1 (p.508 #102) Express the perimeter as a single
rational expression.
Groups 2 & 3: The two formulas: Young’s Rule C 
DA
and
A  12
x
x5
x
x6
Cowling’s Rule C  D  A  1 approximate dosage of a drug
24
prescribed to children. In each formula, A is the child’s age in years, D is an adult dosage and C
is the proper child’s dosage. The formulas apply for ages 2 through 13, inclusive.
GROUP 2 (p.508 #94) Use Young’s Rule to find a child’s dosage for a 10-year old child and a 3year old child. Find the difference in these dosages and express the answer in a single rational
expression in terms of D. Then describe what your answer means in terms of the variables in the
model.
GROUP 3 Use Cowling’s Rule to find the difference in a child’s dosage for a 10-year old child and
a 3-year old child. Find the difference in these dosages and express the answer in a single
rational expression in terms of D. Then describe what your answer means in terms of the
variables in the model.
Page 9
MATH085 In-Class Assignment
Chapter 9
9.1 Finding Roots
GROUP 1 (p.556 #86) The formula
v  2.5r
models the maximum safe speed, v in mph, at
which a car can travel on a curved road with radius of curvature r, in feet. A highway crew
measures the radius of curvature at a highway exit ramp as 360 feet. What is the maximum safe
speed?
GROUP 2 (p.556 #87) Police use the formula
v  20 L
to estimate the speed of a car, v in
miles per hour, based on the length, L, in feet of its skid marks upon sudden braking on a dry
asphalt road. A motorist is involved in an accident. A police officer measures the car’s skid marks
to be 245 feet long. Estimate the speed at which the motorist was traveling before braking. If
the posted speed is 50 mph and the motorist said that she was not speeding, should the officer
believe her? Explain.
GROUP 3 (p.556 #89) Please read what is said on page 556 concerning the line graph. The data
for one of the two groups shown by the graphs can be modeled by
y  2.9 x  36 where y is
the head circumference, in centimeters, at age x months, 0  x  14 . (a) According to the
model, what is the head circumference, in centimeters at birth? (b) According to the model,
what is the head circumference at 9 months? (c) According to the model, what is the head
circumference at 14 months? Use a calculator to round the nearest tenth of a centimeter. (d)
Use the values in parts (a) through (c) and the graphs on page 556 to determine whether the
model describes healthy children or those with severe autistics.
9.2 Multiplying and Dividing Radicals
GROUP 1 The algebraic expression
2 5L
is used to estimate the speed of a car, in miles per
hour, prior to an accident based on the length of its skid marks L, in feet. Find the speed of a car
that left skid marks 40 feet long and write the answer in simplified radical form.
GROUP 2 The time, in seconds, that it takes an object to fall a distance d, in feet, is given by
the algebraic expression
d
16
. Find how long it will take a ball dropped from the top of a building
320 feet tall to hit the ground. Write the answer in simplified radical form.
GROUP 3 (p.566 #118) Express the area of the rectangle that has a length of
width of
5 feet as a square root in simplified form.
ALL GROUPS Simplify:
(p.565 #83)
75
15
(p.565 #96)
3
250
Page 10
(p.566 #105)
3
27
8
15
feet and
MATH085 In-Class Assignment
9.3 Operations with Radicals
Groups 1 & 3: Draw and label a picture to represent the problem. Write an expression for
perimeter and one for area for each polygon, in simplified radical form.
GROUP 1 (p.571 #87) A square with sides measuring radical 3 inches plus radical 5 inches.
GROUP 3 (p.572 #91) A right isosceles triangle with legs measuring radical 2 inches and
hypotenuse measuring 2 inches.
GROUP 2 (p.572 #95) The bar graph on page 572, shows the percentage of full-time college
students in the U.S. who had jobs for four years. The data can be described by the mathematical
model J  1.4 x  55  (20  1.2 x ) , where J is the percentage of full-time college students with
jobs x years after 1975. (a) Simplify the model. (b) Use the simplified form to find the
percentage of college students who had jobs in 2005. Give your answer in simplified radical form
and then find the approximation rounded to the nearest percent. How does this compare with
the number on the bar graph on page 572?
9.4 Rationalize the Denominator
GROUP 1 (p.578 #83) Do you expect to pay more taxes than were withheld? Would you be
surprised to know that the percentage of taxpayers who receive a refund and the percentage of

taxpayers who pay more taxes vary according to age? The formula P  x 13 
x
 models the
5 x
percentage, P, of taxpayers who are x years old who must pay more taxes. (a) What percentage
of 25-year olds must pay more taxes? (b) Rewrite the formula by rationalizing the denominator.
(c) Use the rationalized form of the formula to find the percentage of 25-year olds who must pay
more taxes. Do you get the same answer? If so, does this prove that you correctly rationalized
the denominator? Explain.
GROUP 2 (p.579 #85) The early Greeks believe that the most pleasing of all rectangles were
the golden rectangles, whose ratio of width to height is
w
2
. Rationalize the denominator

h
5 1
for this ratio and then use a calculator to approximate the answer to the nearest hundredth.
GROUP 3 (p.579 #99) Simplify
2 
1
2
Page 11
MATH085 In-Class Assignment
9.5 Radical Equations
GROUP 1 (p.586 #55) The rate at which firefighters spray water on a fire is dependent upon the
nozzle pressure. The formula f  120 p models the water’s flow rate, f, in gallons per minute,
in terms of the nozzle pressure, p, in pound per square inch. What nozzle pressure is needed to
achieve a water flow rate of 840 gallons per minute?
GROUP 2 (p.586 #59) The bar graph on page 586 shows the percentage of overweight adults in
the U.S. for 1980 through 2004. The formula p  3.6 t  46 models the percentage of Americans,
p, who were overweight t, years after 1980. According to the formula, what percentage were
overweight in 2004? Give your answer in exact form, and then round to nearest tenth of a
percent. Does this over or underestimate the bar graph data? If this trend continues, when will
66% U.S. adults be over weight?
GROUP 3 Two tractors are removing a tree stump from the ground. If two forces, A and B, pull
at right angles to each other, the size of the resulting force, R, is given by the formula:
R
A2  B 2 . Tractor A exerts 300 pounds of force. If the resulting force is 500 pounds, how
much force is tractor B exerting in the removal of the stump? (Make a drawing that represents
the action in this problem.)
9.6 Rational Exponents
1
3
GROUP 1 The formula v   p  models the wind speed, v, in miles per hour, needed to
 0.015 
produce p watts of power from a windmill. How fast must the wind be blowing to produce 120
watts of power?
GROUP 2 According to the AMA, the percentage of potential employees testing positive for
1
2
3
3
illegal drugs is on the decline. The formula P  73t  28t models the percentage, P, of people
t
applying for jobs who tested positive t years after 1986. (a) What percentage of people applying
for jobs tested positive for illegal drugs in 1995? (b) Using this formula, how many in 2000?
GROUP 3 (p.592 #44 & 55) Simplify:
(a)  64 

2
3
Page 12
 25
(b)  x
 x 6 5 x 35





5
MATH085 In-Class Assignment
Chapter 10
10.1a Solving Quadratic Equations using Square Root Property
GROUP 1 (p.607 #77) A square flower bed is to be enlarged by 2 meters on each side. If the
larger square has an area of 144 square meters, what is the length of the original square?
GROUP 2 (p.608 #80) A machine produces open boxes using square sheets of metal. The
figure, on page 608, illustrates that the machine cuts equal-sized squares measuring 2 inches on
a side from the corners and then shapes the metal into an open box by turning up the sides. If
each box must have a volume of 200 cubic inches, find the size of the length and width of an
open box.
GROUP 3 (p.607 #71) If the area of a circle is
36
square inches, find its radius. (You should
have this memorized: the formula for area of a circle is A  r 2 ).
10.1b Solving Quadratic Equations using Square Root Property
GROUP 1 (p.607 #67) A ladder is leaning up against the side of building. The bottom of the
ladder is 10 feet from the base of the building, and the top of the ladder reaches a height of 8
feet. How long is the ladder?
GROUP 2 (p.607 #69) A baseball diamond is actually a square with 90-foot sides. What is the
distance between home plate and second base?
GROUP 3 In a 27-inch square television set, the length of the screen’s diagonal is 27 inches.
Find the measure of the sides of the screen. Express your answer in exact form, and then
approximate to the nearest inch.
Everyone, after working on your group problem try this one: A small skateboard
company’s revenue is modeled by P  q  20 2  200 where P is the company’s daily profit
and q is the quantity (number) of skateboards produced each day. Solve for q when P = 136.
Explain your answer in the context of the problem.
10.2 Solving Quadratic Equations by Completing the Square
GROUP 1 (p.613 #10) Complete the square for the binomial x 2 
1
x then factor the
3
resulting perfect square trinomial.
GROUP 2 (p.613 #30) Solve the quadratic equation
2x2  x  1  0
GROUP 3 (p.613 #34) Solve the quadratic equation
3x 2  2 x  4  0
Page 13
by completing the square.
by completing the square.
MATH085 In-Class Assignment
10.3a Quadratic Formula
GROUP 1 (p.623-624 #57) The bar graph on page 623 shows the number of visitors, in
millions, to America’s national parks from 1988 to 2006. The data can be modeled by
N  0.095 x 2  1.74 x  60 , where N is the number of visitors in millions after 1988. (a) According
to the model, how many visitors to national parks were there in 2006? Round to nearest tenth of
a million. Does the model over or underestimate the actual number? By how much? (b) If trends
continue, in which year will there be 41 million visitors to national parks?
GROUP 2 A person standing on a platform fires a gun straight up into the air from a height of
50 feet. The formula h  16t 2  110t  50 describes the bullet’s height above the ground, h, in
feet, t seconds after the gun is fired. How long will it take for the bullet to hit the ground? Round
your answer to the nearest tenth of a second. What do the numbers in the formula represent in
the context of the problem?
GROUP 3 (p.624 #60) The length of a rectangle is 2 meters longer than the width. If the area is
10 square meters, find the rectangle’s dimensions and the length of the rectangle’s diagonal
(round to the nearest tenth of a meter). Draw the rectangle and label the length, width and
diagonal.
10.5 Graphs of Quadratic Equations
GROUP 1 (p.640 #50) You have 120 feet of fencing to enclose a rectangular plot that borders
on a river. If you do not fence the side along the river, find the length and width of the plot that
will maximize the area. What is the largest area that can be enclosed? (make a sketch)
GROUP 2 (p.640 #49) The formula
y  0.22 x 2  0.50 x  7.68
models the number of
households, y, in millions, participating in the Food Stamp Program x years after 1999.
According to this model, how many households received food stamps in 1999? Does this over or
underestimate the actual data shown on the bar graph on page 640? By how much? Use the
formula to determine the year that the number of households was at a minimum. Compare this
to the bar graph.
GROUP 3 (p.641 #68) A parabola has x-intercepts at 3 and 7, a y-intercept at -21, and (5, 4)
for its vertex. Write the parabola’s equation.
Page 14