Honors Algebra 2 - Unit 6 HW Answer Key
HW #1
8. answers may vary – all points on the x-axis should look like (1, 0, 0) for example. You will have a non-zero number
for the x-coordinate and y and z will be zero. The same is true for points on the y-axis and z-axis. Points not on the
axes won’t have any coordinate values of zero. Here is a sample answer:
8a. y and z are zero
8b. the other 2 coordinates will be zero
9. (2, -5)
10a. 9
10b. V = 4(N – 1) + 1 or V = 4N – 3; this is arithmetic
11a. ≈1.204
11b. ≈1.613
11c. 6
11d. ≈2.004
1
25
x
12b. 2
y
1
12c. 2 2
x y
12a.
b10
12d.
a
13a. x
13b.
6
6
or
2
( x  1)( x  2)
x  3x  2
HW #2
21a.
21b.
21c.
21d.
22a.
22b.
22c.
(0, 10, 0), (0, 0, 4)
(8, 0, 0), (0, 6, 0), (0, 0, 12)
(0, 0, 4), (0, 0, -4), (2, 0, 0), (-8, 0, 0)
(0, 0, 6)
a line
they do not intersect
they do not intersect
24. It is not the parent. The second equation does not
have a vertical asymptote, and it has a maximum value,
while y  1 does not (or there is no way to get the graph
x
1
1
of y 
by shifting or stretching the graph of y 
25a. x 
23a. y = -2(x + 4)2 + 2
23b. y 
1
x2
23c. y = -x3 + 3
x
x2  7
b
3
25b. x 
b
5a
25c. x 
b
1 a
27. It is the log5(x) graph shifted 2 units to the right.
29a.
29b.
29c.
29d.
-7
-102
-102
-132
HW #3
x3
2x  1
1
39b.
x3
35.
39a.
40a. x = 8 or x = 1
40b. 1 does not check…it is an extraneous solution
41a. x = -4 or x = 5/2
41b. x = -4, 2, 3
36. yes
41c. x = 0, -1, 7/2, -4/3, 13, or -7
37. Yes, because if the numbers are the same, the
41d. set each of the factors equal to zero and solve the
exponent you would use to get them should be the same,
corresponding equations
given the same base.
43. x = 3, y = 1, z = 3
1
38. y  -x + 4, y  x
3
HW #4
51. (1, -2, 4)
53. x = 7
54a. they both equal 16, but this is a special case…for
example, 53  35
54b. yes because log 16 = log 16
54c. yes because they have the same solutions
54d. yes because they have the same solutions
55a. x = 6.5
55b. x = -3.75 or x = 5
56a. y 
1
x5
3
56b. y = 2x + 5
56c. y  
1
15
x
2
2
56d. y = 2x
57a. y = -x2 + 4x
57b. y  5  x  3
HW #5
71. x = -1, y = 3, z = 5
72. y = 3x2 – 5x + 7
75a. x = 12y
75b. yx = 17
75c. 2x = log1.75 y
75d. 7 = logx 3y
58a.
58b.
HW #6
84. yes, Hannah is correct. 4(x – 3)2 – 29 = 4x2 – 24x + 7
and 4(x – 3)2 – 2 = 4x2 – 24x + 34
85a. y = 2(x – 2)2 – 1, vertex (2, -1), axis of symmetry x = 2
85b. y = 5(x – 1)2 – 12, vertex (1, -12), axis of symmetry x
=1
80. x = -1, y = 3, z = 6
81. y = 2x2 – 3x + 5
82a. 24 = ba
82b. 7 = (2y)3x
82c. 5x = log2 3y
82d. 6 = log2q 4p
HW #7
96. In 2 = 1.04x, the variable is the exponent, but in 56 =
x8 the exponent is known so you can take the 8th root
97. x > 100 because 102 = 100
98. 0 < b < 1
102a. yes
102b. it is not a function
1
8
1
99b.
x
99a.
99c. m ≈ 1.586
99d. n ≈ 2.587
99e. x  b
1
a
1
100. 2 2 
2 and 2 1 
1
2
102c. not necessarily
102d. Functions that have inverse functions have no
repeated outputs. A horizontal line can intersect the
graph in no more than one place (in other words, the
original function must pass a horizontal line test)
102e. Yes. For example, a sleeping parabola is not a
function, but its inverse is a function.
HW #8
113a. x ≈ 5.717
113b. x ≈ 11.228
115.
log 5 7
log 5 2
118. They are correct. Vertex (2.5, -23.75), line of symmetry x = 2.5
119a. f(x) = 4(x – 1.5)2 – 3, vertex (1.5, -3), line of symmetry x = 1.5
119b. g(x) = 2(x + 3.5)2 – 20.5, vertex (-3.5, -20.5), line of symmetry x = -3.5
120a. consider only x ≥ -2 or x  -2
120b. Depending on the original domain restriction, y 
120c. x ≥ -7 and y ≥ -2 or x ≥ -7 and y  -2
x7
x7
 2 or y  
2
3
3
HW #9
127a. y = 40(1.5)x
127b. when x = -9 or 9 days before the last day of Oct (Oct 22)
130. the graph should show a decreasing exponential function which will have an asymptote at room temperature;
temperature of the drink won’t drop below room temperature
131. y= x2 – 6x + 8
133a. x ≈ 6.24
133b. x = 5
HW #10
139a. x = ½
139b. any number except 0
139c. x = 1023
140a. x = 2.236
140b. x = 4.230
140c. x = 0.316
140d. x = 2.021
140e. x = 3.673
141a. 16
141b. 12
141c. 124 = 20736
141d. 54
141e. no, they are not inverses (if they were, the answers to parts c and d would have to be 2)
142. square it and subtract 5; he dropped in a 76
143. c(x) = x2 – 5