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Deriving the quadratic formula
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Deriving the quadratic formula
1.
From Whence
The Quadratic Formula? Don Simmons © D. T. Simmons, 2009 1
2.
Deriving the Quadratic
Formula Everybody taking algebra eventually learns the quadratic formula. 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
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