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parabola
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Parts of a parabola Two panels showing function graphing concepts: Panel A illustrates plotting an arbitrary function f by selecting values of t and marking corresponding f(t) points; Panel B graphs the specific parabola f(t) equals t squared, with plotted points showing how t values map to t squared. Both graphs use dashed lines to connect points to the axes for clarity. Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape. Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated. A diagram of a double cone intersected by two green planes labeled PP (picture plane) and RP (reality plane), illustrating projected conic sections in projective geometry, with the apex and a point Omega marked. Illustration showing how a parabolic satellite dish antenna focuses incoming transmission signals onto a single point, with red lines representing signal paths reflecting off the dish surface toward the feedhorn. Insets provide a side view and a three-quarter view, highlighting the role of the paraboloid shape in signal reception. Archimedes' parabolic segment calculation Diagram showing the elements of a bullet's parabolic trajectory in ballistics, with a rifle at the left, labeled lines for line of sight, line of departure, and the curved bullet trajectory passing through mid-range height and hitting a target at 200 yards. Two graphs compare projectile motion. Panel A shows a parabolic path starting high on the Z axis and curving downward to the X axis. Panel B shows a parabolic path starting at the origin, rising upward, then curving back down to the X axis, illustrating an initial upward velocity. Figure 7: Parabola (see text).
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parabola: References & Edit History

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Article History

Type Description Contributor Date
Modified link of Web site: Mathematics LibreTexts - Parabolas. Oct 08, 2026
Article revised and updated. Sep 02, 2026
Added top questions and media. Mar 16, 2026
Add new Web site: Mathematics LibreTexts - Parabolas. Dec 12, 2025
Add new Web site: National Center for Biotechnology Information - PubMed Central - Fast parabola detection using estimation of distribution algorithms. Sep 20, 2025
Add new Web site: East Tennessee State University - The Parabola (PDF). May 29, 2025
Article thoroughly revised. Apr 03, 2025
Add new Web site: Education Resources Information Center - Parabolas: Connection between algebraic and geometrical representations (PDF). Feb 26, 2025
Add new Web site: Universities of Leeds - White Rose Research Online - The Circle Theorem for Nonlinear Parabolic Systems. Jan 04, 2025
Add new Web site: Lamar University - Parabolas. Oct 11, 2024
Add new Web site: Academia - The Parabola (PDF). Jul 16, 2024
Add new Web site: Western Kentucky University - How to recognize a Parabola. Jun 07, 2024
Add new Web site: BCcampus Open Publishing - Parabolas. Dec 15, 2023
Add new Web site: Atlantic Canada Pressbooks Network - Algebra and Trigonometry OpenStax - The Parabola. Nov 02, 2023
Add new Web site: California State University Northridge - Parabolas. Jun 16, 2023
Add new Web site: California State University Northridge - Parabolas. Mar 25, 2023
Add new Web site: Khan Academy - Parabola. Jan 27, 2023
Add new Web site: OpenStax - College Physics 2e - The Parabola. Sep 13, 2022
Add new Web site: Story of Mathematics - Parabola οΏ½ Properties, Components, and Graph. Jul 28, 2022
Corrected display issue. Jun 13, 2019
Add new Web site: Math is Fun - Parabola. Apr 17, 2017
Added new Web site: University of St Andrews - Parabola. Mar 06, 2008
Added new Web site: Math Pages - Parabola Through Four Points. Mar 06, 2008
Added new Web site: Kent State University - Parabola. Mar 06, 2008
Added new Web site: Integrated Publishing - The Parabola. Mar 06, 2008
Added new Web site: Xah Lee Web - Parabola. Mar 06, 2008
Added new Web site: Wolfram Mathworld - Parabola. Mar 05, 2008
Article added to new online database. Jul 20, 1998
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