Finding equation of parabola

Question

I have a group of points from a graph.

When I connect the points I get a shape which looks like the one's of the function f(x) = a / x .

How can i precisely find the equation of the shape ?

Answer 1

To find the polynomial interpolation of $n$ points $(x_0,y_0)$, $(x_1, y_1)$, ..., $(x_n,y_n)$ is $$p(x)=\frac{(x-x_1)(x-x_2)\cdots(x-x_n)}{(x_0-x_1)(x_0-x_2)\cdots(x_0-x_n)}\cdot y_0+\frac{(x-x_0)(x-x_2)\cdots(x-x_n)}{(x_1-x_0)(x_1-x_2)\cdots(x_1-x_n)}\cdot y_1+\ldots+\frac{(x-x_0)(x-x_1)\cdots(x-x_{n-1})}{(x_n-x_0)(x_n-x_1)\cdots(x_n-x_{n-1})}\cdot y_n$$

$$p(x)=\sum_{i=0}^{n}y_i\cdot\prod_{0\leq j\leq n,j\neq i}\frac{x-x_j}{x_i-x_j}$$

There is no unique function that passes through a set of points. Interpolation only gives an approximate function. Even this depends on the kind of interpolation you choose. If you don't know interpolation and you have this kind of problem, then I'm guessing you're not asking the right question.

Answer 2

You need three or more points to find the equation of a parabola: Simply substitute the (x,y) of the points into y=ax^2+bx+c and solve simultaneously This method will work for any type of graph, just edit the formula to look contain the correct number of "x-values"