Editing Quadratic function (section)

==The square root of a univariate quadratic function==
The [[square root]] of a univariate quadratic function gives rise to one of the four conic sections, [[almost always]] either to an [[ellipse]] or to a [[hyperbola]].

If <math>a>0,</math> then the equation <math> y = \pm \sqrt{a x^2 + b x + c} </math> describes a hyperbola, as can be seen by squaring both sides. The directions of the axes of the hyperbola are determined by the [[ordinate]] of the [[minimum]] point of the corresponding parabola <math> y_p = a x^2 + b x + c .</math> If the ordinate is negative, then the hyperbola's major axis (through its vertices) is horizontal, while if the ordinate is positive then the hyperbola's major axis is vertical.

If <math>a<0,</math> then the equation <math> y = \pm \sqrt{a x^2 + b x + c} </math> describes either a circle or other ellipse or nothing at all.  If the ordinate of the [[maximum]] point of the corresponding parabola
<math> y_p = a x^2 + b x + c</math> is positive, then its square root describes an ellipse, but if the ordinate is negative then it describes an [[Empty set|empty]] locus of points.