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:
“This house was designed and constructed with the freedom of stroke of a forester’s axe, without other compass and square than Nature uses.”
—Henry David Thoreau (1817–1862)
“Not marble nor the gilded monuments
Of princes shall outlive this powerful rime;
But you shall shine more bright in these contents
Than unswept stone, besmeared with sluttish time.
When wasteful war shall statues overturn,
And broils root out the work of masonry,
Nor Mars his sword nor war’s quick fire shall burn
The living record of your memory.”
—William Shakespeare (1564–1616)
“The function of comedy is to dispel ... unconsciousness by turning the searchlight of the keenest moral and intellectual analysis right on to it.”
—George Bernard Shaw (1856–1950)