The Square Root of A Quadratic Function
The square root of a quadratic function gives rise to one of the four conic sections, almost always either to an ellipse or to a hyperbola. If then the equation describes a hyperbola. The axis of the hyperbola is determined by the ordinate of the minimum point of the corresponding parabola .
If the ordinate is negative, then the hyperbola's axis is horizontal. If the ordinate is positive, then the hyperbola's axis is vertical.
If then the equation describes either an ellipse or nothing at all. If the ordinate of the maximum point of the corresponding parabola is positive, then its square root describes an ellipse, but if the ordinate is negative then it describes an empty locus of points.
Read more about this topic: Quadratic Function
Famous quotes containing the words square, root and/or function:
“If magistrates had true justice, and if physicians had the true art of healing, they would have no occasion for square caps; the majesty of these sciences would of itself be venerable enough. But having only imaginary knowledge, they must employ those silly tools that strike the imagination with which they have to deal; and thereby, in fact, they inspire respect.”
—Blaise Pascal (1623–1662)
“There is a certain class of unbelievers who sometimes ask me such questions as, if I think that I can live on vegetable food alone; and to strike at the root of the matter at once,—for the root is faith,—I am accustomed to answer such, that I can live on board nails. If they cannot understand that, they cannot understand much that I have to say.”
—Henry David Thoreau (1817–1862)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)