Looking for the function of a curve that starts at 0,0

Question

I'm sorry I don't know all the right words to ask...I am a working professional that finished all my math courses decades ago!

I am trying to develop a metric score card for my company's information security program. I want to gradually increase a score (y value) as more and more devices are out of compliance (x value). In short, I am looking for the function of a curve that starts a 0,0 and goes at least to (or crosses over) 100,100 - where the curve looks somewhat like a quarter circle - like this.

I feel like the following function is close, but the line is almost linear as the x value increases, which is not what I want.

$y=(x^2/100)$

Answer 1

The equation of the quarter-circle like in your picture is $$y=100-\sqrt{100^2-x^2}$$

Answer 2

Welcome to the site !

Since I suppose that you want that points $(0,0)$ and $(100,100)$ be perfectly reproduced, the simplest model would be $$y=100 \left(\frac{x}{100}\right)^a$$ Now, you need to tune $a$ using regression.