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Quadratic Formula: Solve by Completing the Square

Understand how to solve quadratic equations with the quadratic formula, including examples such as 6x^2 + 9x + 2 = 0 and x^2 + 6x + 9 = 0. Learn about the discriminant and why some equations have 2 real solutions, others have 1, and some have none.

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Quadratic Formula: Solve by Completing the Square

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  1. Quadratic Formula

  2. Solve by Completing the Square ax2 + bx + c = 0 a The Quadratic Formula

  3. Solve using the Quadratic Formula 6x2 + 9x + 2 = 0 a = 6 b = 9 c = 2 X = -0.27 X = -1.23

  4. Solve using the Quadratic Formula x2 + 6x + 9 = 0 a = 1 b = 6 c = 9

  5. Solve using the Quadratic Formula 3x2 + 7x = -5 3x2 + 7x +5 =0 a = 3 b = 7 c = 5 NO Solutions

  6. Why do some quadratic equations have 2 real solutionssome have 1 real solution and some have no solutions?

  7. 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 no solutions

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

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