How to find an equation for a graph?

[JoshHolloway]

Is there some way to draw a graph on my TI-89 (titanium) and have it find the equation for the graph? Is there any way to do this? Sorry if this is a stupid question, I am still new to math. I only learned algebra a year ago, and am currently in Calc 1.

 

[JoshHolloway]

Can this not be done? I would love to know the answer to this.

 

[Jameson]

Ok, you can input points in the statistics editor and then make a best fit curve. You'll have to choose the curve type, such as linear, quadratic, cubic etc. and it can do a best fir curve.

 

[JoshHolloway]

Is the statistic editor the same thing as the "Y= Editor"?

 

[JoshHolloway]

I can not figure out how to do that. Could you please explain the procedure? I can not find it in the owners manual, nor can I find a website about this topic.

 

[1800bigk]

what are the points of the graph you want to find an equation for?

 

[z-component]

First of all, this isn't a stupid question if you don't have the manual. Secondly, there is no "statistics editor." The only editors on the 89 are the Data/Matrix Editor, Window Editor, Program Editor, Text Editor, and Y= Editor.

If I understand correctly, you want to hand draw a graph and find an equation for it, but unfortunately this is not possible on any TI calculator.

Working with linear regression and best-fit lines is a little different.

 

[z-component]

The method Jameson has mentioned is working still with best-fit curves. Can you clarify if this is what you want?

 

[JoshHolloway]

I do have the manual, I just can't find where it explains how to do this. The only phrases or expressions I can think of that would fit this inquiry would be "find equation". So that is what I looked up in the index, but it is of course not there. There is no specific graph I need the equation for, I just have been wondering how this is done for a while now, and I thought I might as well figure out how to do it. I guess just for curiosities sake is the reason. But I think that I would use this function someday. I am not sure how, but it seems like I could use it.

 

[JoshHolloway]

If I understand correctly, you want to hand draw a graph and find an equation for it...

This is EXACTLY what I want to do.

 

[moose]

It all depends on what type of graph it is...

Some graphs are quite simple, for example sin graphs. Others however, would be difficult to figure out just by looking at...

 

[JoshHolloway]

What would be great is if I could somehow figure out a method to finding the equation to a line that is tangent to a specified point on any graph. That would be just super.
But seriously, the reason I was wondering this is because recently I was thinking about how carpenters find exact areas of things that are iregularly shaped. Like how they find the square footage of a floor that they need to lay carpet down on, but the wall is curvy (like a simple non-linear graph). I know this is the area problem from the integral concept; but how is that used in every day life if you don't know the equation? Do carpenters have softare that they simply draw a close aproximation of the shape of the floor into, then the program takes the integral of that shape (graph) and spits out the area?
I figured that this might be a function on my mighty powerful calculator, at least for rather simple shapes. So that is why I am asking this question.

 

[JoshHolloway]

My dad is actually a carpenter, but I think he just estimated the area of floors and shapes like this. And I am sure that would suffice for most jobs, but what if the floor was very big. Or what if the precision of the area was important, like on a jet airplane. I guess this requires 3 dimensions, but I am pretty sure that engineers don't figure out the euation to a graph that is the same shape as the object then take the integral of the shape. They probably just draw the picture into a software package and it finds the area for them. But wouldn't the program have to find the equation to the graph?
I am sure there are many experienced engineers in here that do this stuff every day. Please let me know how this is done. And how can I find and equation to a graph. I am an engineering student, but I am only in my first semester of college currently. So I have not taken any engineering specific or advanced mathematics courses yet.

 

[JoshHolloway]

So how could I do this?

 

[jtbell]

In your case (finding the tangent to a curve that you draw) the quickest way would probably be to draw a careful graph of the curve on paper, using good graph paper, then draw the tangent (straight) line at the point in question, then read off two points on that line and calculate the slope via the good old "slope = rise/run" formula.

There is no simple answer to "how to do this numerically". There are whole courses at the college/university level devoted to the general subject of "numerical methods", which includes curve-fitting to data points. There are different approaches to curve-fitting, depending on the source and quality of your data.

 

[JoshHolloway]

In your case (finding the tangent to a curve that you draw) the quickest way would probably be to draw a careful graph of the curve on paper, using good graph paper, then draw the tangent (straight) line at the point in question, then read off two points on that line and calculate the slope via the good old "slope = rise/run" formula.

I was just kidding about finding the equation of a tangent line. As I said earlier, I am in Calculus currently. I want to know how to draw a graph and find the equation to the entire gragh.

 

[JoshHolloway]

So can this be done?

 

[jtbell]

The basic problem is to find an equation for a curve that passes through a set of points. If you're actually drawing a curve, you'll have to digitize points off of it somehow.

If you want something that passes through the points exactly, you probably need a method that uses splines of some kind. This doesn't give you a single equation for the whole curve, but instead a series of equations for pieces of the curve, that fit together smoothly. I once dabbled a bit with cubic splines, but I don't remember much off the top of my head.

If you want a single equation that comes close to most or all of the points, you're looking for curve fitting a.k.a regression methods. These are appropriate if you have experimental data that has natural random "wiggles" in it because of experimental errors. You don't want the curve to include those wiggles. Here you have to make a guess beforehand, from theory, what kind of function might be appropriate: linear? polynomial? exponential? logarithmic? sine/cosine? etc. You can't just fly blind.

Look on university web sites for course materials for "numerical methods" courses. They're usually in either the math or the computer science department. There are probably lecture notes and examples out there somewhere.