Question

I've found four points and am unable to nail down the function that would give them. I know it's something similar to log2(x), but can't nail it down.

The points are: (0.5, 0.5)(1, 1)(2, 3)(2.5, 6.5)

A visual representation can be seen here: http://i.imgur.com/LgZ5T.png

If anyone has an idea of the function that would provide these points, I'd greatly appreciate it.

Also, if you figure it out, lemme know how you did. ^^

Answer 1

No. Its not a log function. Its a parabolic function. Equation will be of the form y^2 = 4ax

Where a= focus of parabola.

Answer 2

So you're saying it's something similar to (x * 4)^0.5 = y? And what would the focus be if the equation were centered on the origin?

Answer 3

Yes ...something similar to x^2 = 4ax. That visual representation is wrong. The parabola will be along the y-axis.
@amistre64 can help!

Answer 4

I'm trying out variations, but it doesn't seem that any sort of parabolic curve will fit these values. Log is much closer, at least in what I'm trying. But hey, if you have any recommendations, I'd appreciate it.

Answer 5

4 points eh, are they all on the parabola?

Answer 6

Thats what I am trying amistre64. The graph seems more like a parabola than a log function...don't you think?

Answer 7

the graph does not match the given points unless you see it from the "y" axis

Answer 8

we can try to form this to the results in a parabola by setting up 3 or more equations of the form ax^2+bx+c = d

Answer 9

there x is the independant and the variables to find are the coefficients

Answer 10

set up a matrix:

(0.5)^2 0.5 1 0.5
1^2 1 1 1
2^2 2 1 3
(2.5)^2 2.5 1 6.5

and row reduce

rref{{(0.5)^2, 0.5,1, 0.5},{1^2, 1,1,1,},{2^2, 2, 1,3},{(2.5)^2, 2.5,1, 6.5}}

if this is reducible than we have a parabola as the result

Answer 11

the last row is inconsistent

http://www.wolframalpha.com/input/?i=rref%7B+%7B%281%2F2%29%5E2%2C+1%2F2%2C1%2C+1%2F2%7D+%2C%7B1%5E2%2C+1%2C1%2C1%7D%2C%7B2%5E2%2C+2%2C+1%2C3%7D%2C%7B%285%2F2%29%5E2%2C+5%2F2%2C1%2C+13%2F2%7D%7D

Answer 12

these will not form a parabola

Answer 13

if they had all been n the same parabola; we would have had a consdition like this:

http://www.wolframalpha.com/input/?i=rref%7B%7B9%2C-3%2C1%2C9%7D%2C%7B4%2C-2%2C1%2C4%7D%2C%7B25%2C5%2C1%2C25%7D%2C%7B100%2C10%2C1%2C100%7D%7D

the last row is all zeros so we have a consistent system

Answer 14

Nevermind gents, I ended doing a flutterton of trigonometry, and figured it out. Thanks for the help!