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katie oliver

on 6 May 2010

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Transcript of Parabolas

Parabola History
Menaecnmus, a pupil of Plato & Eudoxus, attempted to duplicate the cube to find a side of a cube that has a volume double the size of a given cube. He solved it by finding the intersection of the two parabolas x²=y and y²=2x.Later, Apollonius gave the parabola its name after reading Euclid's writings on the conic section. The focus and directrix of the parabola were suggested by Pappus.
Standard Equation Formulas

Famous astronomer Galileo found that any object thrown flys in a parabolic path. Real world examples:
car headlights & flashlights
mirrors in reflecting telescopes
television and radio antennae
human eye Horizontal Graphing Formula:
-centered at origin
-centered at (h,k)

Vertical Graphing Formula:
-centered at origin
-centered at (h,k)
(x-h)²=4p(y-k) A parabola is a set of points (x,y) that are the same distance from a fixed line (directrix) and a fixed point (focus). The vertex is the midpoint of the segment connection focus and directrix. The axis of symetry is the line passing through the focus and vertex.
-vertical parabolas have a vertical aos
-horizontal parabolas have a horizontal aos

The directrix is always parallel to the aos Type:
The type of parabola is determined by the letter that is NOT squared.
-horizontal if (x-h) is not squared
-vertical if (y-k) is not squared |p| in the graphing formula represents the distance from vertex to focus and distance from vertex to directrix.
2|p| is the distance from focus to LRE
4|p| is the length of the LRE segment
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