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The square equation

  1. May 5, 2005 #1
    I just want to see how can the square equation, [tex]a(x + {\frac {b} {2a})^{2} + ({c - {\frac {b^2} {4a}) [/tex], can be optained from

    [tex]ax^2 + bx + c[/tex]

    Can anyone show me how the equation is manipulated to result into the square form?
     
    Last edited: May 5, 2005
  2. jcsd
  3. May 5, 2005 #2
    your expression isn't quite right, but the correct one is easy to derive:

    [tex]ax^2+bx+c = a\left( x^2 + \frac{b}{a}x\right) + c = a\left(x^2 + \frac{b}{a}x + \frac{b^2}{4a^2} - \frac{b^2}{4a^2}\right) + c[/tex]

    [tex] = a\left(x^2 + \frac{b}{a}x + \frac{b^2}{4a^2}\right) + c - \frac{b^2}{4a} = a\left(x+\frac{b}{2a}\right)^2 + \left(c - \frac{b^2}{4a}\right).[/tex]
     
  4. May 5, 2005 #3
    Thank you!
     
  5. May 5, 2005 #4
    Whats the significance fo this?
     
  6. May 5, 2005 #5
    My math teacher often don't explain the logic of anything and having learned the equation just today I was quite disturbed by it and I wanted to "understand" the equation. That's all. I admit I've been quite silly for not figuring it out...
     
    Last edited: May 5, 2005
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