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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.

$y=(x^2/100)$

Rich
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    How about a perfect quarter circle: $y=-\sqrt{100^2-x^2}+100$? – David Mitra Aug 13 '21 at 07:18
  • @DavidMitra - Sounds like what I am looking for, but that function gives me an inverted parabola when I graph it at https://www.transum.org/Maths/Activity/Graph/Desmos.asp – Rich Aug 13 '21 at 07:29
  • The link is the graph of $y=x^2-5$... – David Mitra Aug 13 '21 at 07:31
  • That's the default function the page auto fills out when you arrive on the page. When I replace that function with yours in to the graph, it is just an inverted parabola – Rich Aug 13 '21 at 08:25
  • Be careful that "$100^2-x^2$" is under the "square root bar" (there probably is some technical term for that). – David Mitra Aug 13 '21 at 08:32
  • Ah, you are right, that was my mistake! Thank yoU! – Rich Aug 13 '21 at 08:33

2 Answers2

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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.

Claude Leibovici
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  • Thanks for helping, Claude! This looks to give me the same curve from the function I listed above. I think what I am looking for is a line that when it hits 100,100 its going vertical - a line that looks like a like a quarter circle from 0,0 to 100,100. – Rich Aug 13 '21 at 07:14
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The equation of the quarter-circle like in your picture is $$y=100-\sqrt{100^2-x^2}$$

David Quinn
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