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### Usefulness of General Form of Quadratic Equation

```Date: 03/24/2005 at 10:50:03
From: Warren

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

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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