Parabolas definitions Flashcards
Parabolas definitions
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Parabola A U-shaped curve formed by slicing a cone with a tilted plane, characterized by a focus and a directrix. Conic Section A curve obtained by intersecting a cone with a plane, resulting in shapes like circles, ellipses, and parabolas. Focus A fixed point inside a parabola, equidistant from the vertex as the directrix, determining the curve's shape. Directrix A fixed line outside a parabola, equidistant from the vertex as the focus, always opposite the opening direction. Vertex The point on a parabola midway between the focus and directrix, representing the curve's maximum or minimum. Axis of Symmetry A line passing through the vertex and focus, dividing the parabola into two mirror-image halves. Standard Form An equation format for parabolas, typically written as (x-h)^2 = 4p(y-k) or (y-k)^2 = 4p(x-h). p Value A parameter in the standard form equation that determines the distance from the vertex to the focus and directrix. Vertical Parabola A parabola that opens upward or downward, with its axis of symmetry parallel to the y-axis. Horizontal Parabola A parabola that opens to the right or left, with its axis of symmetry parallel to the x-axis. Opening Direction The orientation of a parabola, determined by the sign of the p value, indicating up, down, right, or left. Width The distance between points on a parabola, measured as 2|p| units from the focus, indicating how 'wide' the curve appears. Origin The point (0,0) on a graph, often used as the vertex for simplified parabola equations. Equation Coefficient A numerical factor in the standard form equation, used to solve for the p value and determine parabola properties. Smooth Curve A continuous, unbroken line connecting points on a parabola, representing its characteristic U-shape.
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