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Algebra 2 Trig A

Review of Algebra 2 Trigonometry problems involving hyperbolas, circles, ellipses, and parabolas with detailed solutions and step-by-step explanations.

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Algebra 2 Trig A

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  1. Algebra 2 Trig A Final Review 2007

  2. #1 Hyperbola • Center (0, 0) • a = 8, b = 7, c = • Vertices: (+8, 0) • Foci: ( , 0) • Slopes of asymptotes: +7/8

  3. #2 y2 = 121 - x2 • Circle: x2 + y2 = 121 • Center: (0, 0) • Radius = 11

  4. #3 y = 2(x - 2)2 + 1 • Parabola • Center/Vertex: (2, 1) • AOS: x = 2 • DOO: up • Focus: (2, 9/8) • Directrix: y = 7/8

  5. #4 6x2 + 16y2 = 96 • Ellipse: • Center: (0, 0) • a = 4, b = , c = • M vertices: (±4, 0) • Foci: ( , 0) • LMA = 8 • lma =

  6. #5 x2 - 2x + y - 8 = 0 • Parabola: y = -(x - 1)2 + 9 • Center/Vertex: (1, 9) • AOS: x = 1 • DOO: down • Focus: (1, 8 3/4) • Directrix: y = 9 1/4

  7. #6 x2 = 2x + y2 - 4y + 7 • Hyperbola • Center: (1, 2) • a = 2, b = 2, c = • Vertices: (3, 2), (-1, 2) • Foci: (1± , 2) • Slopes of Asymptotes: ±1

  8. #7 x2 +4y2 + 2x - 24y + 33 = 0 • Ellipse • Center: (-1, 3) • a = 2, b = 1, c = • Vertices:(-3, 3),(1, 3) • Foci: • LMA = 4 • lma = 2

  9. #8 x2 + y2 = x + 2 • Circle • Center: (1/2, 0) • Radius= 3/2

  10. #9 Find f(x) + g(x) • f(x) = x2-x+3 g(x) = x+8 • f(x)+g(x) = (x2-x+3) + (x+8) • f(x)+g(x) = x2 + 11

  11. #10 Find f(x) - h(x) • f(x) = x2-x+3 g(x) = x+8 • f(x) - h(x) = (x2 - x + 3) - (3x2+1) • f(x) - h(x) = x2 - x + 3 - 3x2 - 1 • f(x) - h(x) = -2x2 - x + 2

  12. #11 Find f(g(x)) • f(x) = x2-x+3 g(x) = x+8 • f(x) = x2 - x + 3 • f(g(x)) =(x+8)2 - (x+8) + 3 • f(g(x)) = x2 + 16x +64 - x - 8 + 3 • f(g(x)) = x2 +15x + 59

  13. #12 Find f(h(x)) • f(x) = x2-x+3 h(x) = 3x2+1 • f(x) = x2 - x + 3 • f(h(x)) = (3x2+1)2 - (3x2+1) + 3 • f(h(x)) = 9x4+6x2+1-3x2-1+3 • f(h(x)) = 9x4+3x2+3

  14. #13 Find g(f(x)) • g(x) = x+8 f(x) = x2-x+3 • g(x) = x + 8 • g(f(x)) = (x2 - x + 3) + 8 • g(f(x)) = x2 - x + 11

  15. #14 Find h(f(x)) • h(x) = 3x2+1 f(x) = x2-x+3 • h(x) = 3x2 + 1 • h(f(x))= 3(x2 - x + 3)2 + 1 • h(f(x))= 3(x4-2x3+4x2 -3x+9)+1 • h(f(x))= 3x4-6x3+21x2-18x+27+1 • h(f(x))= 3x4-6x3+21x2-18x+28

  16. #15 Find h(g(x)) • h(x) = 3x2+1 g(x) = x+8 • h(x) = 3x2 + 1 • h(g(x)) = 3(x + 8)2 + 1 • h(g(x)) = 3(x2 + 16x + 64)+1 • h(g(x)) = 3x2 + 48x + 192 + 1 • h(g(x)) = 3x2 + 48x + 193

  17. #16 Find f(-3) • f(x) = x2 - x + 3 • f(x) = x2 - x + 3 • f(-3) = (-3)2 - (-3) + 3 • f(-3) = 9 + 3 + 3 • f(-3) = 15

  18. #17 Find h(f(4)) • h(x) = 3x2+1 f(x) = x2-x+3 • f(4) = (4)2 - (4) + 3 • f(4) = 15 • h(x) = 3x2 + 1 • h(15) = 3(15)2 + 1 • h(f(4)) = 676

  19. #18 Find g(h(2)) • g(x) = x+8 h(x) = 3x2+1 • h(2) = 3(2)2 + 1 • h(2) = 3(4) + 1 • h(2) = 13 • g(13) = 13 + 8 • g(h(2)) = 21

  20. #19 Inverse of f(x) = 4x + 5 • y = 4x + 5 • x = 4y + 5 • x - 5 = 4y • x/4 - 5/4 = y

  21. #20 Inverse of g(x) = 3x2 - 12 • y = 3x2 - 12 • x = 3y2 - 12 • x + 12 = 3y2 • x/3 + 4 = y2

  22. #21 f(x)=1/2x+2 g(x)=2x-4 • f(g(x))=1/2(2x - 4) + 2 • f(g(x)) = x - 2 + 2 • f(g(x)) = x

  23. #22 f(x) = 3x-9 g(x) = -3x+9 • f(x) = 3x-9 • y = 3x - 9 • x = 3y - 9 • x + 9 = 3y • x/3 + 3 = y • Not equal to g(x)

  24. #23 {(1,3),(1,-1),(1,-3),(1,1)} • {(3,1),(-1,1),(-3,1),(1,1)} • Domain: 3, -1, -3, 1 • Unique x - coordinates

  25. #24 Simplify • Simplify:

  26. #25 Simplify • Simplify

  27. #26 Simplify • Simplify:

  28. #27 Simplify • Simplify:

  29. #28 Absolute value equation • Solve:

  30. #29 Absolute Value Inequality • Solve:

  31. #30 Find f(-5) • If f(x) = 4x3 - x + 1 • f(-5) = 4(-5)3 - (-5) +1 • f(-5) = -500 + 5 + 1 • f(-5) = -494

  32. #31 Do the math • (8x3 + 2x2 + 3x)÷(2x + 3)

  33. #32 Simplify • Simplify:

  34. #33 Factor: 27a3 + 125b3 • Factor: 27a3 + 125b3 • (3a + 5b)(9a2 - 15ab + 25b2)

  35. #34 Factor: 9x2 - 12x + 4 • Factor: 9x2 - 12x + 4 • (3x -2)2

  36. #35 Factor: 7y - 12x + 4xy - 21 • Factor: 7y - 12x + 4xy - 21 • 7y - 21 + 4xy - 12x • 7(y - 3) + 4x(y - 3) • (y - 3)(7 + 4x)

  37. #36 Factor: 15a3b - 5a2b2 - 10ab3 • Factor: 15a3b - 5a2b2 - 10ab3 • 5ab(3a2 - ab - 2b2) • 5ab(3a2 - 3ab +2ab - 2b2) • 5ab[3a(a - b) + 2b(a - b)] • 5ab(a - b)(3a + 2b)

  38. #37 Simplify: • Simplify:

  39. #38 Simplify: • Simplify:

  40. #39 Simplify: • Simplify:

  41. #40 Solve: • Solve:

  42. #41 Solve: x2 + 441 = 0 • Solve: x2 + 441 =0 • x2 = -441 • x = • x = ±21i

  43. #42 Simplify: (9 - 3i) - (3 + 5i) • (9 - 3i) - (3 + 5i) • 9 - 3 - 3i - 5i • 6 - 8i

  44. #43 Simplify: (5 + 4i)(3 - 7i) • Simplify: (5 + 4i)(3 - 7i) • (5 + 4i)(3 - 7i) • 15 - 35i + 12i - 28i2 • 15 - 23i - 28(-1) • 15 - 23i + 28 • 43 - 23i

  45. #44 Simplify: • Simplify:

  46. #45 Simplify: (7 - 3i)(7 + 3i) • Simplify: (7 - 3i)(7 + 3i) • 49 + 21i - 21i - 9i2 • 49 - 9(-1) • 49 + 9 • 58

  47. #46 Simplify: i10i21i30 • Simplify: i10i21i30 • i10+21+30 = i61 = i4(15)+1 = i1 = i

  48. #47 Simplify • Simplify:

  49. #48 Solve: x2 + 5x + 13 = 0 • x2 + 5x + 13 = 0

  50. #49 Solve: 6x2 + 7x = 3 • Solve:

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