The Physics
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Opus in profectus

Curve Fitting

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Summary

power general form description appearance
0 y = k independent horizontal, straight line
1 y = kx direct non-horizontal straight line through the origin
2 y = kx2 square vertical parabola with vertex at the origin
3 y = kx3 cube  
−1 y = k/x inverse rectangular hyperbola
−2 y = k/x2 inverse square  
−3 y = k/x3 inverse cube  
½ y = kx square root horizontal parabola with vertex at the origin
y = kx cube root  
Power relationships summarized
Polynomial relationships summarized
order general form name
0   y = a   constant
1   y = a + bx   linear
2   y = a + bx + cx2   quadratic
3   y = a + bx + cx2 + dx3   cubic
4   y = a + bx + cx2 + dx3 + ex4   quartic
5   y = a + bx + cx2 + dx3 + ex4 + fx5   quintic
     ⋮           ⋮     
n  
n
y = a0x0 + a1x1 + a2x2 + a3x3 +… =  Σ aixi
i = 1
  nth order polynomial