Parabola

To form a parabola, you would start with a line and a point off to one side. The line is called the "directrix"; the point is called the "focus". The parabola is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola up the middle) is called the "axis of symmetry". The point on this axis which is exactly midway between the focus and the directrix is the "vertex"; the vertex is the point where the parabola changes direction.

The "vertex" form of a parabola with its vertex at (h, k) is: regular: y = a(x – h)2 + k sideways: x = a(y – k)2 + h
The conics form of the parabola equation (the one you'll find in advanced or older texts) is: regular: 4p(y – k) = (x – h)2 sideways: 4p(x – h) = (y – k)2
The relationship between the "vertex" form of the equation and the "conics" form of the equation is nothing more than a rearrangement: y = a(x – h)2 + k y – k = a(x – h)2 (1/a)(y – k) = (x – h)2 4p(y – k) = (x – h)2