Quadratic function Guide, Meaning , Facts, Information and Description
In
mathematics, a
quadratic function is a
polynomial function of the form
- ,
where
a is nonzero. It takes its name from the
Latin quadratus for
square, because quadratic functions arise in the calculation of areas of squares. In the case where the
domain and
codomain are
R (the
real numbers), the
graph of such a function is a
parabola.
If the quadratic function is set to be equal to zero, then the result is a quadratic equation.
The square root of a quadratic function gives rise either to an ellipse or to a hyperbola. If a>0 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 a<0 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.
A bivariate quadratic function is a second-degree polynomial of the form
-
Such a function describes a quadratic
surface. Setting
f(x,y) equal to zero describes the intersection of the surface with the plane
z=0, which is a
locus]] of points equivalent to a
conic section.
Roots
The roots, or solutions to the quadratic function, for variable x, are
- .
For the method of extracting these roots, see quadratic equation.
See also
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