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ALGEBRA II
WS 209
NAME _____________________________
PERIOD _____ DATE ________________
TRUE OR FALSE. NO NEED TO CORRECT THE FALSE.
____False______________1. All rational numbers are also integers.
_____True_____________2. (7 + 3i) + (8 – 2i) = (8 – 2i) + (7 + 3i) is the commutative
property of complex numbers.
_____False_____________3. Graphing a quadratic function can always provide the exact
roots of the function.
_____False_____________4. ( m – 6)2 = m2 + 36.
_____False_____________5. The graph of y = x is a vertical line.
CIRCLE THE BEST ANSWER.
6. The irrational number:
7. The conjugate of 6 – 5i:
81
or
48
-6 + 5i
or
6 + 5i
8. If a quadratic has a double root, what is true about the number of solutions?
One real Solution
or
9. Synonym for the roots of a quadratic equation:
Two real Solutions
x-intercepts or
10. A quadratic function with roots of 5 and –2:
y = (x + 5)(x – 2) or
PERFORM THE OPERATIONS WITHOUT A CALCULATOR:
11. i6
12. (-2 – 5i) + (8 – 10i)
6-15i
-1
15. (4 + 5i)2
-9+40i
4i 3
y = (x – 5)(x + 2)
13. (3 + 6i) – (-5 – 10i)
8+16i
14. (5 + 2i)(3 – 7i)
29-29i
17.
y-intercepts
48
18.
3i 5
45
3  2i
4  5i
22 + 23i
41
16.
19.
7 3
12  75
FIND THE DISCRIMINANT OF THE FOLLOWING AND DESCRIBE THE
NATURE OF THE SOLUTIONS.
20.
x2 + 2 = 3x
1, 2 solutions
21.
3x2 = 7x + 8
-47, no real solutions
-----------------------------------------------------------------------------------------------------------SOLVE AND CHECK EACH OF THE FOLLOWING: WORK MUST BE
SHOWN!
22.
x2 + 2x2 + 1 = -1 – x
-1 ± i 23
6
24.
2x2 + 20x – 22 = 0
x=-11, 1
2x2 – 7x – 4 = 0
x=-0.5, 4
23.
10x – 6 = 5x2
5±i 5
x=
5
25.
26. The manager of a factory has found that the output at the factory can be
modeled be the function T(n) = -0.2n2 + 8n – 24, where n is the number of
workers at the factory on a given day and T(n) is the output.
a.
b.
56
Find the number of workers needed in order to maximize the output.
(Two points)
20
What is the maximum output at this factory? (Two points)
27. A football is thrown by a quarterback and follows the path given by
h ( x ) = -0.0095x 2 + x + 7 , where h is the height of the ball in feet and x is
the horizontal distance the ball has traveled in fet. If any height less than
10 feet can be caught or knocked down, at what distances from the
quarterback can the ball be knocked down?
X<3.09 feet or x> 102.1 feet
28. A buisness offers tours to the Amazon. The profit, P, that the company
earns for x number of tourists can be modeled by
P ( x ) = -25x 2 +1000x - 3000 . How many people are needed for a profit of
at least $5000?
11.06 £ x £ 28.94
29. Lisa has a swimming pool that is 60 ft. by 20 ft. She wants to put a
sidewalk around it of uniform width. Lisa lives in the country, but she only
want the total area taken up to be 2000 sq. ft. How wide should the
sidewalk be?
X= 4.49 feet
30. Solve 2x - 8 = 7
X=15/2, x= 1/2