Usefulness of General Form of Quadratic EquationDate: 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/ |
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