Place the origin of the coordinate system on the ground level under at the vertex of the parabola, 
i.e. under the top point of the arc.


Let x be horizontal axis and y be the vertical axis, directed up.


Then the equation of the parabola is  y = -ax^2 + 15.


Then the span of the parabola is from x = -90 m to x= 90 m.


Hence,  y = 0 = ,   or


    a*90^2 = 15,

    a =  =  =  = .


Thus the equation of the parabola is  y = .   ANSWER