Quadratic Equation

Date: 7/10/96 at 18:20:45
From: Anonymous
Subject: "Quadratic" Equation

Why is a quadratic equation... quadratic?  My math tutor asked me to 
find out and I have no idea where to start looking!

Date: 7/11/96 at 8:58:56
From: Doctor Paul
Subject: Re: "Quadratic" Equation

Good question!  Quadratic equations are very important in math.  A 
quadratic equation is one with form as follows:

a*x^2 + b*x + c

pronounced: A X squared plus B X + C

An example of a quadratic equation would be:  x^2 +2x + 1
In this particular case (and this case only!) a=1, b=2, and c=1

The fun comes when you set quadratic equations equal to zero and try 
to solve for values of x that satisfy the equation.  There is a very 
famous formula that should help you solve quadratic equations but I'll 
let your tutor tell you what that is.  

One final note:  Learn quadratic equations!  They will appear in 
Algebra II, Pre-Calculus, all the way through Calculus and on into 
Differential Equations.  You certainly want to learn them now before 
you fall behind!

If you have any other questions, feel free to contact Dr. Math again.

-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 7/14/96 at 21:14:58
From: Doctor Mike
Subject: Re: "Quadratic" Equation

Hello,

I am another Dr. in the same mathematics clinic with Dr. Paul, who
sent you an excellent answer to your quadratics question. One thing
that makes mathematics so interesting is that there can be different
answers to the same question.  This usually comes from looking at the
question in different ways, and the different answers can all be 
right.

Dr. Paul and I consulted on your case yesterday, and you will be glad
to know that both our fees are covered by insurance.
  
I wanted to write back to you with a different answer.  Dr. Paul's
information will, I hope, be useful to you.  His advice to be sure you
learn quadratics well, including the quadratic formula, is right on
the money.  My point of view for this question is more oriented to the
use of the words involved.  Perhaps this is part of what you wanted.
  
When a quadratic polynomial expression a*x^2 + b*x + c is set equal
to zero the result is a quadratic equation.  The reason that the word
"quadratic" is used here is that the prefix "quad-" or "quadr-" in the
English language usually means four (4) of something. This is because
of our language's roots extending back to Latin, among other places.

The simplest 4-sided figure is the square, and the highest power of x
in a quadratic equation is x squared, or x to the power two (2).  The
word squared meaning power of 2 relates to the fact that the area of a
square whose edge length is x is exactly x squared.  Anyway, the word
quadratic, with its quad- prefix, is used because of this connection 
between power 2 in the equation, and its relation to 4-sided squares. 

I hope both answers, together, cover what you were interested in. 

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/