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Deriving the quadratic formula

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Deriving the quadratic formula from the quadratic equation

Deriving the quadratic formula from the quadratic equation

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  • 1. From Whence The Quadratic Formula? Don Simmons© D. T. Simmons, 2009 1
  • 2. Deriving the Quadratic FormulaEverybody taking algebra eventually learns the quadraticformula. But few know where it comes from.This presentation will help you understand how to get … From: ax 2 bx c 0 b b2 4ac To: x 2a© D. T. Simmons, 2009 2
  • 3. Deriving the Quadratic Formula• Begin with the quadratic equation… ax 2 bx c 0• Set the leading coefficient to one. ax 2 bx c 0 a b c x2 x 0 a a© D. T. Simmons, 2009 3
  • 4. Deriving the Quadratic Formula• Isolate the variables on one side of the equation by moving the c value. 2 b c x x 0 a a b c x2 x a a© D. T. Simmons, 2009 4
  • 5. Deriving the Quadratic Formula• Complete the square. b c x2 x a a 2 2 b b c b x2 x a 2a a 2a© D. T. Simmons, 2009 5
  • 6. Deriving the Quadratic Formula• Create a common denominator. 2 b b2 b2 4a c x x a 4a 2 4a 2 4a a• Combine the fractions 2 b b2 b2 4a c x x a 4a2 4a 2© D. T. Simmons, 2009 6
  • 7. Deriving the Quadratic Formula• Rewrite in exponential form. 2 b b2 b2 4a c x x a 4a 2 4a 2 2 b b2 4a c x 2a 4a 2© D. T. Simmons, 2009 7
  • 8. Deriving the Quadratic Formula• Apply the square root property 2 b b2 4a c x 2a 4a 2 b b2 4a c x 2a 2a© D. T. Simmons, 2009 8
  • 9. Deriving the Quadratic Formula• Isolate x. b b b b2 4a c x 2a 2a 2a 2a b b2 4a c x 2a© D. T. Simmons, 2009 9
  • 10. Deriving the Quadratic Formula• Done! 2 b b 4a c x 2a© D. T. Simmons, 2009 10