IViath 1090.04 Exam 02
Spring 2013
Name
S O(Lth0r
Student ID Number:
Instructions:
• Please remove headphones and hats during the exam
• Show all work, as partial credit will be given where appropriate. If no
work is shown, there may be no credit given.
• All final answers should be written in the space provided oii the exam and
in simplified form. ‘When needed give your answer as an exact amount,
, except for dollar amounts
2
i.e., a fraction or symbolic expression like e
which should be rounded to the nearest cent.
• CALCULATORS ARE NOT ALLOWED ON THIS EXAM
• This is a “closed notes/closed book” exam You are not allowed any
outside aids during this exam. If you have papers at your desk during
the exam you will be given a zero on the exam.
-
• If your phone is out during the exam it will be considered a
cheating offense put your phone away!
-
22 March 2013
Exam 02, Page 2 of??
MathlO9O.004
WRITE YOUR ANSWERS ON THE LINES PROVIDED
1.
2 + bx + c
(a) Suppose you are given the equation a
for finding the solutions to this equation.
(b) Solve using any method:
5x
x(x-3)- (x’-3)o
52
—
16x + 3
=
0. Write the quadratic formula
0
f
2. A company needs to borrow 81.50.000. For tax and related reasons. the company wants
to pay 7.3% interest on this loan. There are three lenders for this money. The first
charges 6%, the second charges 7%, and the third charges 10%. The company is going
to borrow twice as much from the first lender as from the third. How much should the
company borrow from each lender?
Write the system of equations described by this system
DO NOT SOLVE
,‘5o, aDo
/t flJf:
7
3
7o
S
-
,n OLLI? t
0 C 00
0
/1?
ô u,, t 1i? t25
/ 0 952J
/t
0
0
7
‘ô,ooo
_/D
Xc2
.O3(/0,000)/OSO
0
0 0 0
22 March 2013
Exam 02, Page 3 of??
MathlO9O.004
3. Graph the parabola described by the following equatioll:
f(x)
_2i2
=
+ 8x
—
7.
(a) Transform this equation from standard form to “parabola form” by Completing
the Square:
x-
-
_
L_()] [(x)
-
x_
2(
y
-
(b) Based on the standard form and parabola form of the given equation, fill in the
information below:
a
h=Z;k=J
Coefficients:
c
Vertex:
(x,y)
() I)
(x,y)=
(o,—)
=
Axis of Symmetry:
y-intercept
Concave Up or Concave Down?
Vertex
a
Max
or
C-on
d-o
Mm?
Stretched or Shrunk Lengthwise?
/-&=
Width 2 Location
Width 4 Location
k -t-1
/
-
—/
‘Ci)
-
22 March 2013
Exam 02, Page 4 of??
I\Iat h 1090.004
(c) Graph the parabola and axis of symmetry on the coordinate plane below:
1:0
I
I
I
I
.1
-
,
z
::zz:
:::::
7
:zzzE::
z
C
tLü174
—-,,
1
EEIZEEEEZEEZEZEZZEEE
—1L.--
-.
C
22 March 2013
Exam 02, Page 5 of??
MathlO9O.004
4. Given the revenue and cost functions below:
R(t)
C(t)
120t
=
+ 40t + 1000
=
where t is the quantity of units produced and sold.
(a) What is the maximum profit?
()-
—
ct)=
t2Dt
/tL+*/00OJ
—/OOO
_/OO
L-°()
-
z
—?O
2
+/oo)
—
/OOo 4/o
—
i
OO
(b) How many units must be sold to obtain this maximum profit?
O
6 It//7
7-L-
/TZt
ii 1UU77
PJ)
Exam 02, Page 6 of??
MathlO9O.004
5. Given the following rational function:
f()
=
22 March 2013
answer the following questions:
[
4
poin
yo
(a) What is the Domain of this function?
(b) What are the Roots of this function?
p
-7 )(--)
(c)
What is the y
P(o)
-
&
intercept of this function?
=
(d) “Limits”:
oc:
As x
c2
X
f()
:2Y
0
Asx-oo:f(x)
(e) “Events”: What
2
are
the x values
of
the “Events” described by this system?
=
(f) Graph these events on a number line below and determine whether the function is
positive or negative in each region.
SHOW YOUR WORK
e
0
—I’D
-I
P(io
r42(Io)
Jo
22 March 2013
Exam 02, Page 7 of??
MathlO9O.004
6. Based on your answers to the questions above:
(a) What are the vertical asymptotes, if any, of this system?
x=O
(b) What are the horizontal asymptotes.if any, of this
system?
(c) In what region(s) is the function positive?
x&,-)
(d) In what regions(s) is the function negative?
X
7. Now that you have answered the cluestions above, graph the function:
Lz:zzL:
ZZZZZE
----
-\-
“--
\
—
%
E E
E E EE
E
\i’
V.A.:
X3
-H
I
Exam 02, Page 8 of??
IViath 1090.004
22 March 2013
8. Graph the following piecewise function on the coordinate plane below:
(2x—2,
C
x>2
(1)
—3<x<2
(2)
x<—3
(3)
6
::::E:J7:z::
::
EL : :
E
-1--
-
C
LTLZL.
‘V
0
Iath1O9O.OO4
Exam 02, Page 9 of??
Intentionally Left Blank
22 March 2013
Math1090.004
Exam 02, Page 10 of??
Scratch Paper
22 March 2013
C
0
0