Four standard parabolas exist: y^2=4ax (right), y^2=-4ax (left), x^2=4ay (up), x^2=-4ay (down). All have vertex at origin and latus rectum length 4a. The parameter 'a' equals the focus-to-vertex distance and the vertex-to-directrix distance. The latus rectum passes through the focus perpendicular to the axis with endpoints at parameters t=1 and t=-1. The semi-latus rectum 2a frequently appears in formulas. For shifted parabolas (y-k)^2=4a(x-h), the vertex shifts to (h,k) but all properties remain. The general quadratic y=ax^2+bx+c is a parabola with vertical axis; completing the square reveals the vertex at (-b/(2a), (4ac-b^2)/(4a)). Similarly, x=ay^2+by+c is a parabola with horizontal axis.