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 (-$\frac{b}{2a}$, $\frac{4ac-b^2}{(4a)}$). Similarly, x=$ay^{2+by+c}$ is a parabola with horizontal axis.