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(Exercises for Chapter 2: Polynomial and Rational Functions)
E.2.1
CHAPTER 2:
Polynomial and Rational Functions
(A) means “refer to Part A,” (B) means “refer to Part B,” etc.
(Calculator) means “use a calculator.” Otherwise, do not use a calculator.
SECTION 2.1: QUADRATIC FUNCTIONS
(AND PARABOLAS)
1)
The graph of the equation
y
=
x
2
±
2
x
±
8
is a parabola. (AD)
a)
Does the parabola open upward or downward?
b)
Find the vertex of the parabola.
c)
Find the axis of symmetry for the parabola.
d)
Find the
y
intercept of the parabola.
e)
Find the
x
intercept(s) of the parabola, if any.
f)
Use c) and d) to find another point on the parabola.
g)
Graph the parabola in the
xy
plane.
2)
Repeat Exercise 1, tasks a)e) for the parabola with equation
y
=
±
6
x
2
±
33
x
±
15
.
(Calculator) (AD)
3)
Repeat Exercise 1, tasks a)e) for the parabola with equation
y
=
x
2
±
4
x
+
7
.
(AD)
4)
The graph of the equation
y
=
x
2
+
8
x
+
10
is a parabola. (E)
a)
Find the Standard Form (or Vertex Form) of the equation of the parabola.
b)
Does the parabola open upward or downward?
c)
Find the vertex of the parabola.
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E.2.2
5)
Repeat Exercise 4 for the parabola with equation
y
=
±
4
x
2
+
24
x
±
37
. (E)
6)
Repeat Exercise 4 for the parabola with equation
y
=
2
x
2
±
14
x
+
27
. (E)
7)
Find an equation for the parabola that has vertex
6,
±
3
()
and that contains the
point
3,
±
5
. (F)
8)
Profit.
The profit
P
(in dollars) for WidgetCo is given by:
P
or
Px
=
±
50
x
2
+
700
x
±
2000
,
where
x
is the number of widgets produced and sold. Assume that the domain of
P
is
0,
±
²
³
)
, and assume that every widget produced is sold. (A, B)
a)
What is the profit if no widgets are produced and sold?
Hint: The company loses money then.
b)
Use a formula to find the number of widgets (produced and sold) for which
profit is maximized.
c)
What is the corresponding maximum profit? (Calculator)
d)
What are the breakeven production levels for the company? That is, how
many widgets are to be produced and sold if the company’s profit is to be $0?
There are two answers; give both.
9)
Projectile.
A projectile is fired over a flat desert. The height of the projectile is
given by:
h
or
ht
=
±
16
t
2
+
80
t
+
384
, where
t
is time measured in seconds since
the moment the projectile is fired. (The height formula is relevant up until the
moment the projectile hits the ground.) Height
h
is measured in feet. (A, B)
a)
What is the height of the projectile at the moment that it is fired?
b)
Use a formula to find the length of time it takes (since it was fired) for the
projectile to reach its maximum height.
c)
What is the corresponding maximum height? (Calculator)
d)
How long does it take for the projectile to hit the ground (from the moment
the projectile was fired)?
(Exercises for Chapter 2: Polynomial and Rational Functions)
E.2.3
SECTION 2.2: POLYNOMIAL FUNCTIONS OF
HIGHER DEGREE
1)
For each function
f
in a)d) below, find
lim
x
±²
fx
()
and
lim
x
±²³
. (AD)
a)
f
, where
() =
5
x
3
±
4
x
2
+
9
b)
f
, where
3
x
4
+
x
3
±
1
2
x
2
±
7
x
c)
f
, where
±
x
6
+
15
x
5
d)
f
, where
14
x
2
±
2
x
7
2)
How many turning points (TPs) can the graph of
y
=
have, if
f
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This note was uploaded on 09/08/2011 for the course MATH 141 taught by Professor Staff during the Fall '11 term at Mesa CC.
 Fall '11
 staff
 Math, Calculus, Rational Functions

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