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The quadratic equation in the wheat example is found
by a transformation raising X to the power 2 so that
W = X ^ 2 and then performing a
quadratic regression of Y on W with the result: Y = 0.000126 W ^ 2  0.0120 W + 3.80 and hence: Y = 0.000126 X ^ 4  0.0120 X ^2 + 3.80 which is now no longer a second degree (quadratic) equation, but a 4th degree one. 
The cubic equation in the potato example is found by
a transformation raising X to the power 0.5 so that
W = X ^ 0.5 and then performing a
cubic regression of Y on W with the result: Y = 0.537 W ^ 3  4.70 W ^ 2 + 11.2 W + 1.84 and hence: Y = 0.537 X ^ 1.5  4.70 X + 11.2 X ^ 0.5 + 1.84 which is now no longer a third degree (cubic) equation. 
The polynomal case of 1 dependent variable (Y) and 2 independent variables (X and Z) Screen print of the input menu for the polynomial case (1 dependent variable (Y) and 2 independent variables (X and Z). 
The SegReg program found that the 1st independent variable (X) has a higher coefficient of explanation than the second (Z). Therefore the first segemented regression is made for X. The the residuals of Y after the regression on X are used with a segmented regression on the second variable (Z). The mathematical combination of the first and second analysis yields equations of the type Y = A.X + B.Z + C (polynomial) 