The Parabola

Wren Garmon

A parabola is defined as the locus of all points in a given plane that are the same distance from the given point, called the focus, and a given line, called the directrix.

The above graph is the parent graph which has the equation y=x^2. The vertex is at the origin (0,0). The graph always intercepts the coordinates (1,1) and (-1,1).

The standard equation of the parabola is (x-h)^2=4p(y-k). The constant h represents the x-coordinate of the vertex. Whereas the k constant represents the y-coordinate of the vertex. The latus rectum of the graph is represented by 4p .

The parabola can also be represented by two "general form" equations. These equations are y^2+Dx+Ey+F=0, when the directrix is parallel to the y-axis, or
x^2+Dx+Ey+F=0, when the directrix is parallel to the x-axis.

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