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- f(x) = ax2 + bx + c,
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.
- yp = ax2 + bx + c.
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
- yp = ax2 + bx + c
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
- f(x,y) = Ax2 + By2 + Cx + Dy + Exy + F.
The roots, or solutions to the quadratic function, for variable x, are
For the method of extracting these roots, see quadratic equation.
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