The path of a dolphin leaping out of the water can be modelled with the following parametric equations x = 2t m, y = −4.9t² + 10t m where x is the horizontal distance from the point the dolphin jumps out of the water, y is the height above sea level of the dolphin and t is the time in seconds after the dolphin has started its jump. 

a. Find the time the dolphin takes to complete a single jump.

b. Find the horizontal distance the dolphin travels during a single jump.

c. Show that the dolphin’s path is modelled by a quadratic curve.

d. Find the maximum height of the dolphin