To write it in vertex form see: http://web2.0calc.com/questions/re-write-y-x-2-6x-8-in-vertex-form
To plot it either use a graph plotter that will accept a function (e.g. the Desmos graph plotter is a useful on-line plotter: https://www.desmos.com/calculator) or choose a number of values of t, calculate the corresponding values of the function and plot one against the other.
