in geometry, a vertical translation is a translation of a geometric object in a direction parallel to the vertical axis of the cartesian coordinate system.... thumb|300px|the graphs of different antiderivatives of the function f(x)&nbsp;=&nbsp;3x2&nbsp;&minus;&nbsp;2. all are vertical translates of each other. often, vertical translations are considered for the graph of a function. if f is any function of&nbsp;x, then the graph of the function f(x)&nbsp;+&nbsp;c (whose values are given by adding a constant c to the values of f) may be obtained by a vertical translation of the graph of f(x) by distance c. for this reason the function f(x)&nbsp;+&nbsp;c is sometimes called a vertical translate of f(x).. for instance, the antiderivatives of a function all differ from each other by a constant of integration and are therefore vertical translates of each other.. ==references==  
Elementary_geometry