Identify the equation form of the problem !

[honest_denverco09]

Can some one tell me that :How can i identify the form of polynomial functions in different cases . For example, from the table of value :

(1, 38.4) , (1.5, 30) , (2, 19.6) , (2.5 , 7.2)

How can i know that the function that model this table of value is which one in polynomial function to know the general form of it, like it is a quadratic or .... functions ? Will we need to do some steps to know or we just guess ?

Thank you a lot!

[stapel_eliz]

Since they've only given you four points, you're limited in the "conclusions" you can draw. And the methods you can use to find an equation (not necessarily "the" equation) will depend upon the tools they've provided you in your course.

The x-values in the table are equal distances apart, so it's easy to see (by doing the subtractions) that a linear model (something of the form y = mx + b) would probably not be a good idea. (The first two differences are the same, but the third is quite a bit off.)

With four points, however, you can find an exact cubic polynomial, which might be what they're looking for.

What sorts of techniques have they shown you in your book and in class?

Thank you!

[honest_denverco09]

I am getting this math class without the teaching or explaining of the teachers, I just take the books and read them, then i do my homeworks that are given by the teacher as much as i can.

Unfortunately, in my book, it doesn't have the way to solve this problem. ^^! Sorry about that.

But i guess that i can plot these points into calculator and see what kind of the polynomial function. And i did, i identified that this is a quadratic function. Another way that my friend told me is using the "definite square method" to find the sets of difference. And the number of the sets of difference are the degree of the function. And from the degree, we can know what kind of polynomial the table of value representing . But i tried the second way, it is wrong.

The thing that i want to know is how can i know whether some table of values represent the quadratic or cubic functions fast without using calculator ?

[stapel_eliz]

With four points, the exact representation will be a polynomial of degree 3.

In general, with "n" points, the exact representation will be a polynomial of degree n - 1.

[honest_denverco09]

When i tried to find the degree of this, i also get 3, so this problem is probably the cubic function. But it is wrong, because i did see the answer in my teacher book. They state that it is degree of 2, and it is a quadratic function. So, I am confusing!

And when i assume that it is a quadratic function, i substitute 3 points into its quadratic function in general form Ax^2 + Bx + c, then i solve for A, B, and C. I got the function that represent this problem. I did substitute the remanent points into it, they are acceptable !

When we have a table of value and we are supposed to find the equation to represent it, we need to know the form of it, whether a quadratic or a cubic functions ! But i don't know how to know its form ?

[stapel_eliz]

Using only what has here been posted, we can only be sure of a cubic model.

If "the answer" is a quadratic, then there must be other information, such as assumptions, conditions, particular methods, etc. But there is no way for us to know what that other information might be. Sorry!

[honest_denverco09]

Eventually, to know what does the of kind of polynomial function that the table of values represent we just need to find the "Set of Differences" of this values based on y-values. To find the "D" (Set of diff.), we subtract each y-values from the one after it until we get the constants.

In this example, we have the y-coordinates are 38.4, 30, 19.6, 7.2

30 - 38.4 = -8.4
19.6 - 30 = - 10.4
7.2 - 19.6 = -12.4
Those are the 1st "D".

-10.4 + 8.4 = -2
-12.4 + 10 = -2
We did get the CONSTANTS, so we stop right here and our set of Differences is 2
That means this table of values represents the quadratic function (Bino-mial function)
Thank to myself !^^!

[stapel_eliz]

-12.4 + 10 = -2

I had checked the common differences. The above is actually -2.4, not -2. This was part of why, given only the information provided, there was no way to determine "the" quadratic, because the listed points did not lie on one quadratic.

You could find "a" cubic, or find "a" quadratic regression, but not "the" quadratic. Sorry!

[honest_denverco09]

I did have a mistake in my process. Actually i have to minus "-12.4 - (- 10.4)" to get -2, but i did forget the " .4" of 10. Is that your comment about ? Also, i forgot the negative sign of constant "2". So, again i can affirm that this values represent the quadratic function!

30 - 38.4 = -8.4
19.6 - 30 =- 10.4
7.2 - 19.6 = -12.4
Those are the 1st "D".

-10.4 + 8.4 = -2
-12.4 + 10 = -2
We did get the CONSTANTS, so we stop right here and our set of Differences is 2
That means this table of values represents the quadratic function (Bino-mial function)