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Solving Quadratics by Completing the Square & Quadratic Formula

Solving Quadratics by Completing the Square & Quadratic Formula. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: October 24, 2007. X 2 + 6x + 9. x. 1. 1. 1. 1. 1. 1. x. x + 3. Now, complete the square. 1. + 9. 1. 1. x + 3. Jeff Bivin -- LZHS.

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Solving Quadratics by Completing the Square & Quadratic Formula

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  1. Solving QuadraticsbyCompleting the Square&Quadratic Formula By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: October 24, 2007

  2. X2 + 6x + 9 x 1 1 1 1 1 1 x x + 3 Now, complete the square 1 + 9 1 1 x + 3 Jeff Bivin -- LZHS

  3. X2 + 4x + 4 x 1 1 1 1 x x + 2 Now, complete the square 1 4 1 x + 2 Jeff Bivin -- LZHS

  4. X2 + 5x + 25/4 x 1 1 .5 1 1 1 x x + 5/2 Now, complete the square 1 + 25/4 1 .5 x + 5/2 Jeff Bivin -- LZHS

  5. X2 - 6x + 9 x 1 1 1 1 1 1 1 1 1 x - 3 x 1 + 9 1 1 turn 1 square over x - 3 turn 1 square over turn 2 squares over turn 2 squares over turn 3 squares over Jeff Bivin -- LZHS

  6. Solve by Completing the Square x2 + 10x + 8 = 0 (x2 + 10x ) = -8 (x2 + 10x + (5)2) = -8 + 25 (5)2 = 25 (x + 5)2 = 17 Jeff Bivin -- LZHS

  7. Solve by Completing the Square 3x2 + 24x + 12 = 0 3 x2 + 8x + 4 = 0 (x2 + 8x ) = -4 (x2 + 8x + (4)2) = -4 + 16 (4)2 = 16 (x + 4)2 = 12 Jeff Bivin -- LZHS

  8. Solve by Completing the Square 2x2 + 5x - 12 = 0 2 Jeff Bivin -- LZHS

  9. Solve by Completing the Square 2x2 - 12x - 11 = 0 2 Jeff Bivin -- LZHS

  10. Solve by Completing the Square -5x2 + 12x + 19 = 0 -5 Jeff Bivin -- LZHS

  11. Solve by Completing the Square 5x2 - 30x + 45 = 0 5 Jeff Bivin -- LZHS

  12. Solve by Completing the Square 5x2 - 30x + 75 = 0 5 Jeff Bivin -- LZHS

  13. Convert to vertex form y = x2 + 10x + 8 y - 8 = (x2 + 10x ) (5)2 = 25 y - 8 + 25 = (x2 + 10x + (5)2) y + 17 = (x2 + 10x + (5)2) y + 17 = (x + 5)2 - 17 x + 5 = 0 Axis of symmetry: x = -5 Vertex: (-5, -17) Jeff Bivin -- LZHS

  14. Convert to vertex form y = 5x2 - 30x + 46 y - 46 = 5(x2 - 6x ) 5(-3)2 = 45 y - 46 + 45 = 5(x2 - 6x + (-3)2) y - 1 = 5(x2 - 6x + (-3)2) y - 1 = 5(x - 3)2 + 1 x - 3 = 0 Axis of symmetry: x = 3 Vertex: (3, 1) Jeff Bivin -- LZHS

  15. Solve by Completing the Square ax2 + bx + c = 0 a The Quadratic Formula Jeff Bivin -- LZHS

  16. Solve using the Quadratic Formula 3x2 + 7x - 4 = 0 a = 3 b = 7 c = -4 Jeff Bivin -- LZHS

  17. Solve using the Quadratic Formula 6x2 + 9x + 2 = 0 a = 6 b = 9 c = 2 Jeff Bivin -- LZHS

  18. Solve using the Quadratic Formula 5x2 - 8x + 1 = 0 a = 5 b = -8 c = 1 Jeff Bivin -- LZHS

  19. Solve using the Quadratic Formula 6x2 - 17x - 14 = 0 a = 6 b = -17 c = -14 Jeff Bivin -- LZHS

  20. Solve using the Quadratic Formula x2 + 6x + 9 = 0 a = 1 b = 6 c = 9 Jeff Bivin -- LZHS

  21. Solve using the Quadratic Formula 3x2 + 7x + 5 = 0 a = 3 b = 7 c = 5 Two Imaginary Solutions Jeff Bivin -- LZHS

  22. Why do some quadratic equations have 2 real solutionssome have 1 real solution and some have two imaginary solutions?

  23. Now Consider ax2 + bx + c = 0 Discriminant 89 0 -11 If discriminant > 0, then 2 real solutions If discriminant = 0, then 1 real solution If discriminant < 0, then 2 imaginary solutions Jeff Bivin -- LZHS

  24. That's All Folks Jeff Bivin -- LZHS

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