Expert: Paul Klarreich - 5/28/2007

Question
I have a really simple question - what is the formula for calculating the y-value of a turning point of a simple quadratic equation (y=ax^2+bx+c)?? Is it (4ac - b^2)/4a???

Answer
Questioner:   Elizabeth
Category:  Calculus
 
Subject:  Calculus << Not really.
Question:  I have a really simple question - what is the formula for calculating the y-value of a turning point of a simple quadratic equation (y=ax^2+bx+c)?? Is it (4ac - b^2)/4a???
................................................
Hi, Elizabeth,

The x-coordinate of the T.P. of  y = ax^2 + bx + c is:

x = -b/2a

Now substitute that into the function:

y = a(-b/2a)^2 + b(-b/2a) + c
  ab^2    b^2
= ------ - ---  + c
  4a^2    2a

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

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

  - b^2 + 4ac
= ------------
      4a      
RIGHT ON, baby!  You got it.