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Vertex of a Parabola

Date: 04/16/2002 at 22:05:40
From: Chris
Subject: Vertex of a Parabola

What is the quickest annd easiest way to find the y-coordinate of the 
vertex? I know that the x-coordinate is -b/2a. Is the best way to plug 
that value into the equation y = ax^2+bx+c, or is there a special 
formula that will get the answer quicker?


Date: 04/17/2002 at 07:48:25
From: Doctor Floor
Subject: Re: Vertex of a Parabola

Hi, Chris,

Thanks for your question.

Of course we can MAKE the formula by plugging in the x-coordinate:


  y = a(-b/2a)^2 + b*(-b/2a) + c

      a*b^2   b^2
    = ----- - --- + c
      4a^2    2a

       b^2   b^2
    =  --- - --- + c
       4a    2a

          b^2
    = c - --- 
          4a


See also from the Dr. Math archive:

  Completing the Square
  http://www.mathforum.org/library/drmath/view/53102.html 

Here the vertex is derived by completing the square, and is found 
from the formula given in step 5.

If you have more questions, just write back.

Best regards,
- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Basic Algebra
High School Coordinate Plane Geometry

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