math

rosagiang · **Joined:** Thu, 7 Oct 2010 03:57:03 UTC **Posts:** 1

find formula of (1,24),(2,12), (3,?)

Shadow · **Posted:** Fri, 8 Oct 2010 00:56:39 UTC

rosagiang wrote:

find formula of (1,24),(2,12), (3,?)

There can be infinitely many answers to that.

Soroban · **Posted:** Sat, 9 Oct 2010 04:24:00 UTC

Hello, rosagiang!

Quote:

Find formula for: . $(1,24),\;(2,12),\'(3,?)$

The problem is rather silly . . .

Find a function that passes through two points.

Code:

      |
      |   *(1,24)
      |
      |
      |
      |       *(2,12)
      |
      |
      |
  - - + - + - + - - - 
      |   1   2

As Shadow pointed out, there is an infinite number of functions.

$\text{Linear function: }\qquad\quad\; y \:=\:36-12x$

$\text{Quadratic functions: }\;\begin{Bmatrix} y &=& 28-4x^2 \\ y &=& x^2-15x+38 \end{Bmatrix}$

$\text{Cubic functions: }\qquad \begin{Bmatrix}y &=& x^3 - 3x^2 - 10x + 36 \\ y &=& -x^3 + x^2 - 8x + 32 \end{Bmatrix}$

$\text{Exponential functions: }\;y \;=\; \dfrac{48}{2^x}$

. . . . . and so on.

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