Position vs Time. Need help

1. The problem statement, all variables and given/known data
Position vs Time graph is given. It is a perfect parabola. So it has a quadratic equation
Y: Ax^2+Bx+C that fits it perfectly.

(a) Determine acceleration, initial velocity, initial position
(b) Sketch a motion map
(c) Sketch a v vs t graph

My attempt:
initial position: 50 m off the ground (along y axis) from the graph t=0 sec here
initial velocity: slope of the line b/w first and second point?
53-5-50/1 (50 initial position; 53.5 position at t=1 sec and from here on the object goes into free fall)
acceleration: change in velocities/ time taken I’m confused about this because velocity will be 0m/s at 1 sec because the object is about to go into free fall. How do I calculate this?

(b) & (c) I don’t have a clue what motion map is and v vs t can be drawn using position vs time

Thanks!

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