The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Inactive » k12.ed.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Vertex formula?
Replies: 1   Last Post: Jun 27, 2005 12:11 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
Ken Starks

Posts: 20
Registered: 12/6/04
Re: Vertex formula?
Posted: Jun 27, 2005 12:11 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Jennifer Toth wrote:

> Is there a fornula which can give me the y coordinate of the vertex of a
> parabolilc curve?
> I am trying to find a different way other than plugging the value from
> -b/2a back into the equation.

Let us think backwards, using a geometrical transformation of
the parabola, and a chain of basic functions.

If your parabola has its vertex at (P,Q) and is stretched in the
y direction by factor m (negative for 'upside down'), the
quadratic function can be represented by the CHAIN of simple

Start with x
Subtract P
Square that answer
Multiply by m
Add Q
.... thats your y

Now relate these values to what you already know:
P = -b/2a
m = a

Therefore you can substitute ANY value into the
'chain of functions' method and the more usual
'2nd order polynomial' formula, and find Q.

Note that the 'Chain of functions' version is VERY easy
to find the inverse of (taking one root at a time,
obviously) by

Start with y
Subtract Q
Divide by m
Take positive root
( optionally change sign here )
Add P
.... thats your x

It is an algorithm that is very easily performed on a
calculator, not needing any brackets or stored values.

So you can solve f(x) = K for lots of values of K

In my opinion the 'Chain of functions' contains SO MUCH
of the personality of the quadratic that it should replace
the usual formula as a way of solving quadratics. But then
I always did like to think in terms of graphs...

submissions: post to k12.ed.math or e-mail to
private e-mail to the k12.ed.math moderator:
newsgroup website:
newsgroup charter:

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.