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The trajectory of the ball is determined by three things: gravity, air resistance, and spin. This can be seen through the following free body diagrams:
Among the determinants of trajectory, gravity is constant in the downwards direction and air resistance is always against the path of the ball.
Of the different kinds of trajectories, the flat shot or no spin shot is the standard of in terms of trajectory since it will only be affected by gravity and air resistance.
A shot with topspin has a more sharp arc as gravity works with the spin causing the ball to dip. The dip is caused because of a a difference in relative air pressure around the ball. Because the ball is spinning in a certain direction in which the turn of the ball's spin is more favorable of air pressure at the top than the bottom, a mini vacuum is formed to equalize the air speeds. This causes the ball to have a force of spin acting down on the ball which lets it suddenly dip into the table.
A shot with backspin will have somewhat of an opposite effect on the ball than a shot with topspin. Since rotation is going in the opposite direction, the ball's force of spin will be acting against gravity which means that the ball will rise initially and float before eventually dropping once the force of spin dissipates before gravity. This is because a ball with backspin will have have an upward force stronger than gravity that lasts for its magnitude of spin.