How to flatten a simple polynomial

[Bob52]

Is there a way to take a polynomial and “flatten” it. My work is in Cosmology, and I have a polynomial y=(x-a)^2+b that needs to pass through point (c, 100). In this case, the new equation would give results as a percentage. Imagine you have a string lying on a table, shaped as a simple polynomial. You take the string and move it until it is flat or taut. Is there a way to express this mathematically? Thanks

 

[Harry_the_cat]

The general form of a quadratic (polynomial of degree 2) is y = a(x-h)^2 + k where (h, k) is the turning point. The value of "a" determines the "flatness" of the curve. The closer "a" gets to 0, the flatter the curve. Your polynomial needs to have a coefficient in front of x^2 if you want the "flatness" to change.
Does that help?

If your polynomial y = (x-a)^2+b passes through (c, 100) then b=100-(c-a)^2.

If the polynomial y = a(x-h)^2+k passes through (c, 100) then k=100-a(c-h)^2.

 

[Steven G]

If you let |a| get small, then the quadratic will flatten out, where y = a(x-h)^2 + k.

 

[Bob52]

I thought my math problem was much more complicated than the simple solution you gave me. You saved me a lot of time.Thanks so much