A quadratic equation always represents a parabola.Every quadratic form of equation when graphically represented, forms a parabola. When a ball is thrown or kicked, It follows a parabola.
The equation of parabola is can be written as
a, b and c are constants.
(x, y) is an arbitrary point lying on the parabola.
a $\neq$ 0. If a equals zero, then equation will be no more a quadratic equation. Hence it will not represent a parabola.