The Quadratic Formula.
Beautifully created by
Brandon Korn
b  b  4ac
2a
2
What is the quadratic
formula used for???
The Quadratic formula is perfect for solving quadratic
equations
This is the quadratic formula for all you math
folks out there!
 b  b  4ac
x
2a
2
Beautiful
Example #1
Use the quadratic formula… NOW.
8x 2 + 2x - 3= 0
How to
solve:
8x 2 + 2x - 3= 0
a = 8 b = 2 c = -3
x
 2  100
x
16  2  10
 2  10
x
 b  b  4ac
x
2a
2
 2  4  ( 96)
16
16
or
x
x = ½ or x = - ¾
 2  2 2  ( 4  8  3 )
x
2 8
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16
Amazing
Example #2
The quadratic formula should be used in this
equation:
x 2 + 5x + 6= 0
How to
solve:
x 2 + 5x + 6= 0
a=1 b=5 c=6
 b  b 2  4ac
x
2a
 5  5 2  ( 4  1  6)
x
21
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 5  25  ( 24)
x
2
5 1
x
2
51
x
or
2
 51
x
2
x = - 2 or x = - 3
Amazing example #3
Solve the problem using the quadratic formula ok?
8x 2 - 22x + 15= 0
How to
solve:
8x 2 - 22x + 15= 0
22  (484  (480)
x
16
22  4
x
16
a = 8 b = -22 c = 15
 b  b  4ac
x
2a
2
 ( 22)  ( 22)  (4  8  15)
x
2 8
2
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22  2
x
16
or
x = 3/2 or x = 5/4
22  2
x
16
Last but not
least, example #
4!
Use the quadratic formula to solve!!!!
2x 2 +3x - 7= 0
3
How to
x
solve!
2x 2 + 3x – 7 = 0
3
a=2 b=3 c=-7
x
 b  b 2  4ac
x
2a
 3  3 2  ( 4  2  7 )
x
2 2
9  ( 56)
4
65
4
x
 3  8.0622
4
or
x
x = 1.27 or x = - 2.77
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 3  8.0622
4
HELPFUL HINTS MANG!
Always make sure to use a calculator when using the quadratic formula.
Here are some helpful websites.
http://www.purplemath.com/modules/quadform.htm
http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html