Find a function given a set of points

Question

I have a set of points that define a function like this $[(0,6),(1,2),(3,8)]$. I want to find a function $f(x)$ which satisfies these conditions.

Note : I know many people will say there are infinite possibilities, I know that. I just want to find a function with these points I don't care for the other points.

nmasanta · Answer 1 · 2019-06-01T13:15:48.253

1

Since the required function satisfied given three points $(0,6),(1,2) \text{and} (3,8)$, so from there you can conclude that if you want to use a polynomial function then $2^{\text{nd}}$ degree polynomial function is the smallest degree polynomial. So let it be of the form $$f(x)=ax^2+bx+c$$where the constants $a,b, c$ are found by satisfying the points on the function.

Therefore you can follow the rule described by @Cornman.

edited Jun 01 '19 at 13:15

answered Jun 01 '19 at 13:06

nmasanta

9,222

You can't "conclude" that. You can conclude that if you want to use a poiynomial then degree $2$ is the smallest degree. – Ethan Bolker Jun 01 '19 at 13:11
Thanks for the correction @Ethan Bolker – nmasanta Jun 01 '19 at 13:16

score 0 · Answer 2 · answered Jun 01 '19 at 12:37

0

Write $y = ax^2 + bx + c$. Now substitute in your three points. You will have three equations in three unknowns (linear). Solve for $a$, $b$, and $c$.

answered Jun 01 '19 at 12:37

ncmathsadist

49,383

Find a function given a set of points

2 Answers2