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:
“Interpreting the dance: young women in white dancing in a ring can only be virgins; old women in black dancing in a ring can only be witches; but middle-aged women in colors, square dancing...?”
—Mason Cooley (b. 1927)
“In dark places and dungeons the preacher’s words might perhaps strike root and grow, but not in broad daylight in any part of the world that I know.”
—Henry David Thoreau (1817–1862)
““... The state’s one function is to give.
The bud must bloom till blowsy blown
Its petals loosen and are strown;
And that’s a fate it can’t evade
Unless ‘twould rather wilt than fade.””
—Robert Frost (1874–1963)