A golf ball is hit from a point O on a horizontal golf course, and travels at all times in a vertical plane that passes through O. The trajectory of the golf ball is modelled by the equation
where and are respectively the horizontal and vertical displacements, in metres, of the golf ball relative to point O. Upwards is taken to be the positive direction for the vertical displacement.
Write down an appropriate domain for the model, explaining why the domain given is suitable within the context of the question.
Sketch the graph of against , labelling any intersections with the coordinate axes.
Find the maximum height reached by the golf ball.
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