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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

    = c - --- 

See also from the Dr. Math archive:

  Completing the Square

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
Associated Topics:
High School Basic Algebra
High School Coordinate Plane Geometry

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