Editing Quadratic function (section)

===Minimum/maximum===

If <math> 4AB-E^2 <0 ,</math> the function has no maximum or minimum; its graph forms a hyperbolic [[paraboloid]].

If <math> 4AB-E^2 >0 ,</math> the function has a minimum if both {{nowrap|''A'' > 0}} and {{nowrap|''B'' > 0}}, and a maximum if both {{nowrap|''A'' < 0}} and {{nowrap|''B'' < 0}}; its graph forms an elliptic paraboloid. In this case the minimum or maximum occurs at <math> (x_m, y_m) ,</math> where:

:<math>x_m = -\frac{2BC-DE}{4AB-E^2},</math>

:<math>y_m = -\frac{2AD-CE}{4AB-E^2}.</math>

If <math> 4AB- E^2 =0 </math> and <math> DE-2CB=2AD-CE \ne 0 ,</math> the function has no maximum or minimum; its graph forms a parabolic [[cylinder (geometry)|cylinder]].

If <math> 4AB- E^2 =0 </math> and <math> DE-2CB=2AD-CE =0 ,</math> the function achieves the maximum/minimum at a line—a minimum if ''A''>0 and a maximum if ''A''<0; its graph forms a parabolic cylinder.