I am looking for a specific parabola that is horizontal opening toward -x (So a backward C). All of the values in this scenario concern Quadrant 1, and have these rules:
- y-values are whole numbers.
- Point 1 is (185, 1), and is slightly -x,+y from the vertex
- Point 2 is (85, 40), Further -x,+y from the vertex, this is the point of diminishing returns going negative.
- If you multiply the coordinate pair values, the total should get higher as x decreases, and y increases from 1 to 40 (up and to the left), but any multiplication of y=41 and higher should begin to lower.
So:
- (y=1) * (x=185) = 185
- (y=2) * x > 185
- (y=3) * x > 2x
- 4x > 3x
- ...
- (y=40) * (x=85) = 3400
- (y=41) * x < 3400
- (y=42) * x < 41x
- ...
I found this equation which is close: x = 185 - y^2/16, but it caps at the coordinate where y=32 : (121, 32) and begins to lower from there, so I'm not quite there.
I may need to solve this again for two different points, so knowing a tool or process to solve it would be wonderful. But my requirement right now is this specific scenario.