Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Quadratic Formula
Quadratics come in this form:
ax 2 + bx + c = 0
Sometimes it is factorable and finding
the value(s) of x is easy. What do ...
2 + bx + c = 0
ax

   2 + bx + c = 0
ax
a      a     a    a


  2
x     + bx       +c=0
        a         a
x 2
                  + bx       +c=0
                    a         a

          x 2
                 + bx        =0-c
   ...
2                   2
(   x+   b
         2a
           )    =    -c +
                      a     ( )
                   ...
2
                     ( )
x+ b     =±   -c +    b
  2a          a       2a



                    2
x   =±   -c +
       ...
2
x=   ±   -c +
          a
                ( )b
                   2a
                           -   b
                  ...
2
x= -
                          ( )
         b ± 2a    -c +    b
         2a  2a     a      2a


                        ...
2
                               ( )
x=   -       b ± 2a     -c +       b
                         a         2a
          ...
2       2      2
x=   -   b ±   - c (2a) +
                 a           ( )
                              b
              ...
2       2         2
x=   -   b ±   - c 4a +
                 a        ( )
                          b
                    ...
2     2            2
x=   -       b ±   - c 4a +
                     a        ( )
                              b
       ...
2
x = -b ±    b - 4ac
           2a
2
   7x + 14x - 3 = 0

What are the roots of
the above function

               2
  x = -b ±    b - 4ac
             2a

 ...
2
  7x + 14x - 3 = 0

             2
x = -14 ± 14 - 4(7)(-3)
         2(7)


x = -14 ± 196 + 84
         14
x = -14 ± 280
         14


x = -14 ± 16.73
         14
x = -14 ± 16.73
                     14

x1 = -14 + 16.73       x2 = -14 - 16.73
          14                     14
x1 = ...
Upcoming SlideShare
Loading in …5
×

March 9 Quadratic Formula

298 views

Published on

  • Be the first to comment

  • Be the first to like this

March 9 Quadratic Formula

  1. 1. Quadratic Formula
  2. 2. Quadratics come in this form: ax 2 + bx + c = 0 Sometimes it is factorable and finding the value(s) of x is easy. What do you do when it isn't factorable? Can you still solve for x?
  3. 3. 2 + bx + c = 0 ax 2 + bx + c = 0 ax a a a a 2 x + bx +c=0 a a
  4. 4. x 2 + bx +c=0 a a x 2 + bx =0-c a a 2 2= 2 x + bx + a ( ) b 2a -c + a ( ) b 2a
  5. 5. 2 2 ( x+ b 2a ) = -c + a ( ) b 2a 2 2 ( x+ b 2a ) = -c + a ( ) b 2a 2 ( ) x+ b =± -c + b 2a a 2a
  6. 6. 2 ( ) x+ b =± -c + b 2a a 2a 2 x =± -c + a ( ) b 2a - b 2a
  7. 7. 2 x= ± -c + a ( )b 2a - b 2a 2 x= - ( ) b ± -c + b 2a a 2a 2 x= - ( ) b ± 2a -c + b 2a 2a a 2a
  8. 8. 2 x= - ( ) b ± 2a -c + b 2a 2a a 2a 2 ( ) x= - b ± 2a -c + b a 2a 2a
  9. 9. 2 ( ) x= - b ± 2a -c + b a 2a 2a 2 2 2 x= - b ± - c (2a) + a ( ) b 2a (2a) 2a
  10. 10. 2 2 2 x= - b ± - c (2a) + a ( ) b 2a (2a) 2a 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a
  11. 11. 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a
  12. 12. 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a 2 x= - b ± - c 4a + b 2a
  13. 13. 2 x = -b ± b - 4ac 2a
  14. 14. 2 7x + 14x - 3 = 0 What are the roots of the above function 2 x = -b ± b - 4ac 2a 2 7x + 14x - 3 = 0
  15. 15. 2 7x + 14x - 3 = 0 2 x = -14 ± 14 - 4(7)(-3) 2(7) x = -14 ± 196 + 84 14
  16. 16. x = -14 ± 280 14 x = -14 ± 16.73 14
  17. 17. x = -14 ± 16.73 14 x1 = -14 + 16.73 x2 = -14 - 16.73 14 14 x1 = 2.73 x2 = -30.73 14 14 x1 = .2 x2 = -2.2

×