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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>
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