Parabola
Definition

A parabola is a curve that results from graphing a quadratic function. A parabola is symmetric about a line called the axis of symmetry. The vertex of the parabola occurs where the parabola and the line of symmetry intersect.


Parabola

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Dotted Line

A parabola is the locus of points in a plane, equidistant from a fixed point in the plane (the focus) and a fixed line in the plane (the directrix).

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Dotted Line

A parabola occurs when a plane intersects a cone parallel to the axis that generates the cone.

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Dotted Line

A parabola is a curve resulting from graphing a quadratic relation (Ax2 + Bxy + Cy2 + Dx + Ey + F = 0) that has a discriminant (Δ = B2 - 4AC) of zero.




Real World Examples

The path an object makes when thrown through the air traces the shape of a parabola.

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The cross-sectional shape of the mirrored section of most spotlights is parabolic. The light is placed at the focus, to maximize the light output in one direction.

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The cross section of most satellite dishes is parabolic. Rather than "sending out" light, as in the spotlight example above, a satellite dish receives a signal, so that the signal waves come together at the focus of the parabolic dish. The receiver of the satellite dish is placed at the focus of the parabola, to maximize signal reception.