MTH: 140 INTERMEDIATE ALGEBRA
Exam 5 Review
NAME_________________________
Please show all your work and place your final answers in the provided spaces.
Thank you and good luck.
1)
Solve using the square root property: 15 x  48  0
2)
Solve:
2
3x 2  7 x  5  0
a) By completing the square.
b) By using the quadratic formula.
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3)
Solve using U-Substitution
a) x  29 x  100  0
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2
b) x  2 x  6  0
2
4) a) Put h( x)  x  8 x  9 into the form h( x)  a( x  h)  k.
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2
b) Put f ( x)  2( x  3)  5 into the form f ( x)  ax  bx  c.
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2
5) Use the Discriminant of the quadratic formula and state whether the equations can
be factored or if another method of solution has to be used to solve.
a) x  2 x  3  0
2
b) 3 x  6 x  3  0
2
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6) The cost C in dollars of operating a certain concrete–cutting machine is related to
the number of minutes n the machine is run by the function C (n)  2.2n2  66n  655 .
For what number of minutes is the cost of running the machine a minimum? What is
the minimum cost?
7) To create the announcement shown below, a graphic artist must follow two design
requirements. Please see example 10 page. 781.


A border of uniform width should surround the text.
Equal areas should be devoted to the text and the border.
To meet the requirements, how wide should the border be?
x
4
x
6
x
6 + 2x
x
4 + 2x
4
8)
Solve by factoring. Please review section 5.7 for an extended review. Circle your
final answer.
t 3  6t 2  7t  0
 4 x  9  15 x 2  7 x  2   0
x2  2x 1  3x
 x  33x  5  7
8 x 2  10 x  3
4  x  3  x 2  x  3  0
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Given f ( x)  2( x  3) 2  8, answer the following questions:
a) Does the graph of the function open upward or downward?
b) What is the vertex?
c) What is the axis of symmetry?
d) What is the minimum or maximum function value?
e) Does the graph of the function shift to the left or right? How many units?
f) Does the graph of the function shift upward or downward? How many units?
g) Find the x-intercepts.
(Hint: The standard form of the above equation is f ( x)  2 x 2  12 x  10 ).
h) Find the y-intercept.
i) Graph the function on the next page. (Be sure to label all points on your graph.)
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