En matemáticas, una parábola (del griego παραβολή) es la sección cónica de excentricidad igual a 1, resultante de cortar un cono recto con un plano cuyo ángulo de inclinación respecto al eje de revolución del cono sea igual al presentado por su generatriz. El plano resultará por lo tanto paralelo a dicha recta. Se define también como el lugar geométrico de los puntos de un plano que equidistan de una recta llamada directriz, y un punto exterior a ella llamado foco.En geometría proyectiva, la parábola se define como la curva envolvente de las rectas que unen pares de puntos homólogos en una proyectividad semejante o semejanza. La parábola aparece en muchas ramas de las ciencias aplicadas debido a que su forma se corresponde con las gráficas de las ecuaciones cuadráticas. Por ejemplo, son parábolas las trayectorias ideales de los cuerpos que se mueven bajo la influencia exclusiva de la gravedad (ver movimiento parabólico y trayectoria balística).

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A parabola (/pəˈræbələ/; plural parabolas or parabolae, adjective parabolic, from Greek: παραβολή) is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane which is parallel to another plane which is tangential to the conical surface. A third description is algebraic. A parabola is a graph of a quadratic function, y = x2, for example. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point on the parabola that intersects the axis of symmetry is called the "vertex", and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are geometrically similar. Parabolas have the property that, if they are made of material that reflects light, then light which travels parallel to the axis of symmetry of a parabola and strikes its concave side is reflected to its focus, regardless of where on the parabola the reflection occurs. Conversely, light that originates from a point source at the focus is reflected into a parallel ("collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other forms of energy. This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas. Strictly, the adjective parabolic should be applied only to things that are shaped as a parabola, which is a two-dimensional shape. However, as shown in the last paragraph, the same adjective is commonly used for three-dimensional objects, such as parabolic reflectors, which are really paraboloids. Sometimes, the noun parabola is also used to refer to these objects. Though not perfectly correct, this usage is generally understood.

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