Don't treat it as a physics question.
Find the vertex ( )
Then plug in two random numbers (neg and pos) to find the other two points and graph.
(t is just x so look at the x axis for t)
t=0 is when the parabola hits the y axis. (I.e. Just set everything multiplied by t to 0)
max height is just the vertex.
(and for velocity at s=0 just set the equation equal to =0)sorry I thought v=s