MTH: 160 COLLEGE ALGEBRA
Chapter 3 Review
NAME_________________________
Please show all your work on this test and place your final answers in the provided spaces.
Thank you and good luck.
1)
The Principle of Square Roots says that if x 2  k then x  ______________________
2)
Solve:
3)
Simplify:
4)
Simplify:
5 x  35
Ans:_____________________
(i ) 67
Ans:_____________________
2
-540
Ans:_____________________
1
2 x2  3x  6 .
5)
Solve by completing the square:
6)
Solve using U-substitution: 3x  10 x  8  0
7)
Ans:_____________________
Ans:_____________________
Put h( x)  2 x 2  10 x  14 into the form h( x)  a( x  h) 2  k.
Ans:___________________________
2
8)
Put h( x)  
1
2
 x  3  4 into the form h( x)  ax2  bx  c.
2
Ans:___________________________
9) Simplify:
10)
Solve:
2  3i
Ans:___________________________
1  3i
t 1 t 1

1
2
3
Ans:___________________________
3
3
2x  1  3
11)
Solve:
12)
Solve:
13)
Multiply and simplify;
Ans:___________________________
x  2  12  8
3 
Ans:___________________________

25 2  16

4
Ans:___________________________
14)
Solve by using the Quadratic formula; 5 x 2  1  3 x
Ans:___________________________
15)
Use the Discriminant of the Quadratic Formula to determine if you can factor the
4x 2  3  x
quadratic;
Circle YES or NO.
16)
A fourth-grade class decides to enclose a rectangular garden, using the side of the
school as one side of the rectangle. What is the maximum area that the class can
enclose with 32 ft of fence? What should the dimensions of the garden be in order to
yield this area? Don’t forget units.
Length________Width____________
Maximum Area__________________
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17)
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) What is the domain?
f) What is the range?
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. Please properly label all points.
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