vertex

See also answers to previous questions and examples, especially the quiz questions for 9/12/05.

The vertex of the parabola defined by y = f(t) = a t^2 + b t + c has t coordinate

t_vertex = - b / (2 a).

The y coordinate is found by substituting this t coordinate into the function.

In function notation the vertex is located at the point

( -b/(2a), f(-b/(2a) ) ).