The Physics
Hypertextbook
Opus in profectus

Curve Fitting

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Summary

Power relationships summarized
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  
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 y = a0x0 + a1x1 + a2x2 + a3x3 + … + anxn nth order polynomial