Torrence's Math Pages

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Torrence's Math Pages

Algebra 2

CPM online textbook here

Syllabus

Extra Practice for Retakes of math skills quizzes

HW Answers (not solution – just your work and try to identify any errors) – most recent first

Week 7 Key: Microsoft Word – alg 2 week 7 hw key

Week 5 and 6:

Friday, 10/6 and Monday 10/9

hw alg2 chapter 2 closure 1 and 2 answer key

Thursday, 10/5

2-125. See below:

  1. Neither
  2. Neither
  3. Even

2-126. See below:

a.

b.

c.  Neither function is odd nor even.

2-127. y = –0.75(x – 2)2 + 3

2-128. See below:

  1. x: (–1, 0), y: (0, 2), V: (–1, 0), y = 2(x + 1)2.
  2. x: (0, 0), (2, 0), y: (0, 0), V: (1, 1) y = –(x – 1)2 + 1

Wednesday 10/4

2-116. See below:

  1. g(1/2) = −4.75
  2. g(h + 1) = h2 + 2h − 4

2-117. 

  1. y = 2x: (0, 0), y = −0.5x + 6: (0, 6), (12, 0)
  2. It should be a triangle with vertices (0, 0), (12, 0), and (2.4, 4.8).
  3. domain: 0 ≤ ≤ 12, range: 0 ≤ ≤ 4.8 
  4. A =0.5 (12)(4.8) = 28.8 square units

2-118. ≈ 2(x − 5)2 + 2 and y ≈ −0.5(x − 5)2 + 2

2-119. See graph below; y = (x + 1)2 − 81;  x-intercepts: (−10, 0), (8,  0),  y-intercept: (0, −80);  vertex: (−1, −81).

Tuesday 10/3

2-107. See below:

  1. y= (− 2)2 + 3
  2. y= (x − 2)3 + 3
  3. y= −2(x + 6)2

2-108. See below:

  1. domain: all real numbers, range: y ≥ 3
  2. domain: all real numbers, range: all real numbers
  3. domain: all real numbers, range: y ≤ 0

2-109. See below:

  1. compresses or stretches
  2. shifts up or down
  3. shifts left or right
  4. shifts up or down

2-113. See below:

  1. x = ±√(y/2) + 17
  2. x = (y + 7)3 − 5 

Monday 10/2

2-90. See below:

  1. 4.116 · 1012
  2. y = 1.665(1012)(1.0317)t
  3. Explanations vary. Something like it is unlikely that a growth rate would remain constant overtime. GNP tends growth rates tend to be greater at periods of expansion and there are periods of depression. You would have to consider the growth rate a long run average to think of it as constant.

2-95

a. y = (x + 3)2 − 6

b. y = −(x − 3)2 + 6

c.  y = (x + 3)3 – 2

2-139.  y = (x + 3.5)2 – 20.25

2-143. The second graph shifts the first 5 units left and 7 units up and stretches it by a factor of 4. 

Week 4:

Friday 9/29

2-93. Line of symmetry x = 4, vetex at (4, 3)

2-96. He should move it up 6 units or redraw the axes 6 units lower.

2-95.  a. y = 1/(x+2)  b. y = x^2 – 5 c. y = (x − 3)^3 d. y = 2^x – 3  e. y = 3x – 6 f. y = (x +2)^3 + 3

Thursday 9/28

2-81.  possible equation: y = −(4/25)(x − 5)^2 + 8, standing at (0, 0), domain: 0 ≤ x ≤ 10,  range: 4 ≤ y ≤ 8  

2-82.  a. x: (0.5, 0), (−1, 0); y: (0, 1)     b. −0.75 c. (−0.75, −0.125)

2-83. Move it up 0.125 units: y = 2x2 + 3x + 1.125

2-84.  a. 2√6, b. 3√2 c. 2√3, d. 5√3

Wednesday 9/27

2-69.  Possible equations include y = –(1/72)(x – 60)2 + 50, y = –(1/72)x2 + 50, and y = –(1/72)x2 domain and range should include only those values that correspond to the water passing between the boat and the warehouse.

2-72. a/ y = 0.25 · 6^x   b. y = 12 · 0.3^x

2-74. a. stretched parabola, vertex (0, 5) There is a stretch factor of three, so there should be a point at (1, 8)  (-1, 8) b. inverted parabola, vertex (3, –7)

2-69.  Possible equations include y = –(1/72)(x – 60)2 + 50, y = –(1/72)x2 + 50, and y = –(1/72)x2 domain and range should include only those values that correspond to the water passing between the boat and the warehouse.

2-72. a/ y = 0.25 · 6x   b. y = 12 · 0.3x

2-74. a. stretched parabola, vertex (0, 5) There is a stretch factor of three, so there should be a point at (1, 9) b. inverted parabola, vertex (3, –7)

Tuesday 9/26

2-57. B

2-62. a. √61 b. 30º c. tan–1(4/5) d. 5√3

2-63. a. Years; 1.06; 120,000; 120000(1.06)^x b. Hours; 1.22; 180; 180(1.22)^x

Monday 9/25

2-50. a. f(x) = (x + 3)2 + 6, (–3, 6), x = –3 b. y = (x – 2)2 + 5, (2, 5), x = 2   c. f(x) = (x – 4)2 – 16, (4, –16), x = 4 d. y = (x + 3.5)2 – 14.25, (–3.5, –14.25), x = –3.5

2-51.  b^2/4

2-54.   After x is factored out, the other factor is a quadratic equation.  After using the Quadratic Formula the solutions are x = (-23 ± √561)/8 or 0. 

2-55. See below: a. x = 21 b. = 10√5  ≈ 22.4 c. x = 50

Week 3:

Friday 9/22

2-36. See below:

a. (7, –16), y = (x – 7)2 – 16

b. (2, –16) y = (x – 2)2 – 16

c. (7, –9), y = (x – 7)2 – 9

d. (2, –1)

2-39. Let students figure out what form is more useful.

  1. 2
  2. 1
  3. 1
  4. 2
  5. 2
  6. 1
  7. Students check their predictions with a calculator
  8. If the factored version includes a perfect-square binomial factor, the parabola will touch at one point only.

Thursday 9/21

2-23.

a.  vertex at (–3, –8), opens up, vertically stretched.  b. x-intercepts (–5, 0) and (–1, 0);  y‑intercept (0, 10)

2-24. See below:

  1. Tables or graphs should be the same. 
  2. See sample student work below. 
    y = 3(x – 1)2 – 5
    y = 3(x2 – 2x + 1) – 5
    y = 3x2 – 6x + 3 – 5
    y = 3x2 – 6x – 2   (you can also show this by completing square of the one in standard form).

2-25. See below:

  1. y = (x – 8)2 – 5
  2. y = 10(x + 6)2
  3. y = –0.6(x + 7)2 – 2

Wednesday 9/20

2-18. See below:

z = 1.5
z = –18/5
z = 8
z = –3, 2

2-19.  a.  3    b. 1/(x2 y4)    c. √y/x

2-22. Maximum profit is $25 million when n = 5 million.

(I will be expecting to see either completing the square, averaging intercepts, making a table – something more than just answer.)

Tuesday 9/19

1. a. 4  b. 1  c. 16

2. a. (x-3)^2 -11=0  b. (x-2)^2 -3 =0  c. 3(x-2)^2 -16=0  d. -2(x+4)^2 +36

2-5 a. Smallest: 2; Largest: none  b. Smallest: 0; Largest: none  c. Smallest: –3; Largest: none d.  Smallest: none; Largest: 0  e.  At the vertex. (The line of symmetry passes through the vertex, so the x value is at x=-b/(2a)).

2-7 a. Parabola with vertex (3, 0), You should have this graphed.  b. Shifted to the right three units. 

Monday 9/18

1. Expect to see a table filled in and a graph with an asymptote at y=-1, y-int at (0,1) and point at (1,5).  The paragraph will be different than mine but might read something like:  The graph is an exponential function. It has a horizontal asymptote of y=-1.  It has a y-intercept at the point (0,1) and it has one non-rational x-value, x-intercept.  The graph is an increasing function for all values of x. It has no symmetry.  Its domain is all real values.  As x gets very small , y approaches -1 and as x gets very large, y approaches positive infinity.

2. a. D: (-∞, -2] U (2,∞)  R: (-∞,3]U[4,∞)  b. D: [-5,5] R: [-3,4] c. D: (-∞,∞) R: [-1,1]

Week 2:

Friday 9/15

 

 

 

 

 

 

 

 

 

 

 

Thursday 9/14

 

 

 

 

 

 

 

Wednesday 9/13

 

 

1-62.  See below:

D: x = –1, 1, 2; R: y = –2, 1, 2

D: –1 ≤ x < 1; R: –1 ≤ y < 2

D: x ≥ –1; R: y ≥ –1

D: –∞ < x < ∞; R: y ≥ –2

 

 

Tuesday 9/12

Monday, 9/11

Week 1:

Friday, 9/8 – Packet is due to be turned in on Monday!!!

1-18. See below:
a. y depends on x; x is independent. Explanations vary.
b. Temperature is dependent; time is independent.
c. Make sure that time is on x-axis, temperature on y. Temperature increases during day and then comes down over night typically. It is a wave-like pattern.

 

 

 


1-21.
 See below:

 

  1. 1
  2. x = 12
  3. 13
  4. no solution
  5. x = ± ≈ ± 2.55
  6. x = ± ≈ ± 2.65

1-25. Error in line 2: It should be −14, not +14; x = −37. 

 

Thursday, 9/7

1-17. See below:
a. 16
b. 9
c. 478.38

 

 

 

 

Wednesday, 9/6

 

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