CK 12 Algebra II with Trigonometry Concepts 1
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1 10.1 Parabolas with Vertex at the Origin Answers 1. up 2. left 3. down 4.focus: (0, 0.5), directrix: y = focus: (0.0625, 0), directrix: x = focus: ( 1.25, 0), directrix: x = focus: (0, 2), directrix: y = 2 ans CK 12 Algebra II with Trigonometry Concepts 1
2 8.focus: (0.125, 0), directrix: x = ans focus: (0, 0.75), directrix: y = 0.75 ans , p and a have an inverse relationship. 14.see worked out solution key CK 12 Algebra II with Trigonometry Concepts 2
3 15.16 inches above the vertex CK 12 Algebra II with Trigonometry Concepts 3
4 10.2 Parabolas with Vertex at ( h, k ) Answers 1.vertex: ( 1, 6), focus: ( 1, 5.25), directrix: y = 6.75, axis: x = 1 2.vertex: (3, 7), focus: (3, 7.25), directrix: y = 6.75, axis: x = 3 3.vertex: ( 1, 2), focus: (1, 2), directrix: x = 3, axis: y = 2 4.vertex: (3, 0), focus: (0.5, 0), directrix: x = 5.5, axis: y = 0 5.vertex: ( 6, 8), focus: ( 6, 7), directrix: y = 9, axis: x = 6 6.vertex: (0, 5), focus: ( 0.125, 5), directrix: x = 0.125, axis: y = 5 7.ans ans CK 12 Algebra II with Trigonometry Concepts 4
5 9.ans ans , vertex is (4, 3) CK 12 Algebra II with Trigonometry Concepts 5
6 CK 12 Algebra II with Trigonometry Concepts 6
7 10.3 Circles with Center at the Origin Answers 1.ans ans ans CK 12 Algebra II with Trigonometry Concepts 7
8 4.ans ans ans CK 12 Algebra II with Trigonometry Concepts 8
9 no 14. yes 15. no 16. a) b) 3 c) 17. CK 12 Algebra II with Trigonometry Concepts 9
10 10.4 Circles with Center at ( h, k ) Answers 1. D 2. B 3. A 4. C 5.ans ans CK 12 Algebra II with Trigonometry Concepts 10
11 7.ans No, because CK 12 Algebra II with Trigonometry Concepts 11
12 10.5 Ellipses with Center at the Origin Answers 1.vertices: (0, ± 4), co vertices: (±3, 0), 2. vertices: (±5, 0), co vertices: (0, ±2), foci: ans foci: ans vertices: ( ± 8, 0), co vertices: (0, ±1), 4. vertices: (±10, 0), co vertices: (0, ±9), foci: ans foci: ans CK 12 Algebra II with Trigonometry Concepts 12
13 5.vertices: ( ± 7, 0), co vertices: (0, ±2), 6. vertices: (0, ±11), co vertices: (±3, 0), foci: ans foci: ans CK 12 Algebra II with Trigonometry Concepts 13
14 10.6 Ellipses with Center at ( h, k ) Answers 1. center: ( 5, 1), vertices: ( 5, 7) and ( 5, 5), co vertices: (0, 1) and ( 10, 1), foci: 2. center: ( 2, 6), vertices: ( 6, 6) and (4, 6), co vertices: ( 2, 5) and ( 2, 7), foci: 3. center: ( 5, 1), vertices: ( 5, 7) and ( 5, 5), co vertices: (0, 1) and ( 10, 1), foci: 4. center: (0, 6), vertices: (8, 6) and ( 8, 6), co vertices: (0, 1) and ( 0, 11), foci: 5. center: (8, 4), vertices: (8, 1) and (8, 7), co vertices: (7, 4) and (9, 4), foci: 6. center: ( 4, 5), vertices: ( 4, 4) and ( 4, 13), co vertices: ( 2, 5) and ( 6, 5), foci: 7.ans ans CK 12 Algebra II with Trigonometry Concepts 14
15 CK 12 Algebra II with Trigonometry Concepts 15
16 9.ans ans CK 12 Algebra II with Trigonometry Concepts 16
17 10.7 Graphing Hyperbolas Centered at the Origin Answers 1.( ± 3, 0), ( ± 5, 0), 2.(0, ± 5),, 3.( ± 9, 0),, 4.( ± 4, 0),, 5.(0, ± 7),, 6.(0, ± 3),, 7.(0, ± 1),, 8.( ± 8, 0),, 9.(0, ± 4),, 10.ans CK 12 Algebra II with Trigonometry Concepts 17
18 11.ans ans CK 12 Algebra II with Trigonometry Concepts 18
19 13.ans Answers will vary. 15.Foci are and. CK 12 Algebra II with Trigonometry Concepts 19
20 10.8 Writing the Equation of a Hyperbola, Centered at the Origin Answers or 11. or CK 12 Algebra II with Trigonometry Concepts 20
21 12. or 13. or CK 12 Algebra II with Trigonometry Concepts 21
22 10.9 Hyperbolas Centered at ( h, k ) Answers 1.( 5. 1), (0, 1) and ( 10, 1),, 2.(6, 2), (6, 2) and (6, 6),, 3.(3, 2), (3, 5) and (3, 1),, 4.(0, 6), (8, 6) and ( 8, 6),, 5.(8, 4), (7, 4) and (9, 4),, 6.( 5, 4), ( 5, 2) and ( 5, 6),, 7.ans ans CK 12 Algebra II with Trigonometry Concepts 22
23 9.ans ans CK 12 Algebra II with Trigonometry Concepts 23
24 15. CK 12 Algebra II with Trigonometry Concepts 24
25 10.10 General Conic Equation Answers 1.Answers will vary circle, ( 1, 1.5) 11.parabola, (1, 9) 12.ellipse, (2, 0.5) 13.hyperbola, (1.5, 1) 14.parabola, ( 5, 3) 15.hyperbola, ( 2, 7) CK 12 Algebra II with Trigonometry Concepts 25
26 10.11 Classifying Conic Sections Answers 1. circle 2. hyperbola 3. ellipse 4. parabola 5. parabola 6. circle 7. C 8. D 9. A 10. B 11.parabola 12. circle 13.hyperbola 14.parabola CK 12 Algebra II with Trigonometry Concepts 26
27 15. a) ans b) Yes c) d), the ellipses are smaller than the circle CK 12 Algebra II with Trigonometry Concepts 27
28 10.12 Solving Systems of Lines, Quadratics, and Conics Answers 1. ( 1, 8), ( 1, 3), (3, 2.5) 2. (3, 7), 1, 2.75) 3. ( 4, 0), (0, 3.5) 4. ( 6.5, 6.5), (6. 3) 5. (1.722, 0.722), ( 2.322, 3.322) 6. (1.69, 2.155), (0.71, 2.645) 7. ( ± 1.076, 2.843), ( ± 1.610, 1.407) 8. (0, 10), (2, 9) 9. no solution 10. (1, 2), ( 2.67, 4.75) 11. 0, 1, 2, 3, or , 1, 2, 3, or One possibility:, the circle are concentric or do not intersect (2, 2) and ( 2, 2) CK 12 Algebra II with Trigonometry Concepts 28
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