If the path of a baseball is parabolic and is \(200 \mathrm{ft}\) wide at the base and \(50 \mathrm{ft}\) high at the vertex, write an equation that specifies the path of the baseball if the origin is the point of departure for the ball, and the form of the equation is \(y-k=a(x-h)^{2}\), where \((h, k)\) are the coordinates of the highest point of the baseball.