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Usefulness of General Form of Quadratic Equation

Date: 03/24/2005 at 10:50:03
From: Warren
Subject: general form quadratics

When is it useful to know the general form of a quadratic?  Why 
wouldn't I rather know the vertex form or factored form since those 
tell me something about the graph?



Date: 03/24/2005 at 12:06:54
From: Doctor Peterson
Subject: Re: general form quadratics

Hi, Warren.

I assume you're referring to

  y = ax^2 + bx + c

You're right that this form doesn't give a lot of information; but it 
is the form in which you usually _get_ a quadratic function, and it is 
one in which you can easily compare two functions.  Not all such 
functions can be written in factored form (unless you don't mind 
complex numbers), and vertex form is a little cumbersome.

One example that naturally comes in general form is the equation of 
the path of a projectile.  If you are given the speed and angle at 
which it is shot, then a little physics and/or calculus gives you the 
equation in general form, where a represents the effect of gravity, b 
comes from the initial velocity, and c is the initial height.  From 
there, you can massage it a bit and get the vertex, and so on.  But if 
you need to do any further calculations on it, you will probably want 
it back in general form, which is easier to work with (e.g. in 
calculus).

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Basic Algebra

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