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Algebra II Final Review: Solving Equations and Graphing

Review solving equations by elimination, graphing, factoring, quadratic formula, and completing the square exercises in Algebra II.

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Algebra II Final Review: Solving Equations and Graphing

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  1. 1/26/15 Final Review Day 2 Algebra II

  2. Learning Objective • To remember everything in 1stSemetser!

  3. Solve by Elimination (3)( ) (3) 1. (-4)( ) (-4) -12x – 9y - 15z = 69 12x – 20y + 24z = -20 -29y + 9z = 49 54y – 9z = -99 -29y + 9z = 49 25y = -50 y = -2 (9)( ) (9) 6y – z = -11 -29y + 9z = 49

  4. Solve by Elimination (-3, -2, -1) 6(-2) – z = -11 -12 – z = -11 -z = 1 z = -1 -4x – 3(-2) – 5(-1) = 23 -4x + 6 + 5 = 23 -4x + 11 = 23 -4x = 12 x = -3

  5. Solve by Graphing 2. x + 2y = –6 9x + 4y = 16 x + 2y = -6 2y = -x - 6 9x + 4y = 16 4y = -9x + 16

  6. #2 Cont’d (4, –5)

  7. Solve by Graphing 3. -x + 2y > -8 -x + 2y > -8 2y > x - 8

  8. 3. Solve by Graphing

  9. 4. a = 2 Opens up Vertex: x = 1 y = -1 V(1, -1) AoS: x = 1 Min Min Value -1

  10. 4. Domain: All Real #s Range: y -1 –1 0 7 1 V( 1 -1) x y 2 3 1 7

  11. Rewrite in Vertex Form 5. Vertex (4, 3) AoS: x = 4 Opens up Min Value: 3 -32 16

  12. Factor 6. = = (2x – 3) 7. = = (4x + 1) 2x 3 (4 + 6x + 9) 4x 1 (16 -4x + 1)

  13. Factoring Trinomials –18 8. = = = (3x(x – 6) + 1(x – 6)) = (x – 6)(3x + 1) 1 –18 –17

  14. Solve by Quadratic Formula Set = 0 a = 5 b = -2 c = –1 9.

  15. Solve by Completing the Square 10. = – 34 + x - 5 = 25 25

  16. Find the discriminant & determine the nature of the roots. 11. 1 Real Rational Double Root = 0 = = 36 – 36 2 Real Rational Roots = 196 = = 4 + 192 2 Real Imaginary Roots = -231 = = 9 - 240

  17. Write a quadratic equation 12. Roots of -3 and 5 x = -3 x = 5 x + 3 = 0 x – 5 = 0 (x + 3)(x – 5) = 0 – 5 x x –5x 3 3x –15

  18. Solve 4 13. (x – 1)(x + 1)(x – 2)(x + 2) = 0 x = 1, –1, 2, –2 -4 –1 –5

  19. Solve 14. x =

  20. Factor Theorem 15. Find the remainding factors of if one factor is x+4 -4 - 1 = (x – 1)(x + 1)(x + 4)

  21. Simplify 17. = = 16. = = 50

  22. Assignment:Final Review Packet

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