The graph below shows the path of a baseball after it was hi

The graph below shows the path of a baseball after it was hit, where the x-axis shows the number of feet the ball has traveled horizontally and the y-axis shows the height of the ball in feet. What is its greatest height of the ball and how far from home plate (the place where it was hit) will it be when it lands on the ground? (For simplicity assume it starts from the ground level and not the shoulder level of the hitter.) Write an equation for the path of the ball (Be careful! a notequalto 1)

Solution

The graph is not fully clear as the figures on the X and/or Y Axis are not visible. Therefore, we assume that each small line means 1 ft. The path of the baseball is a downwards opening parabola with vertex at (50,60). Hence the greatest height of the ball is 60 feet. Further, it will be 100 feet from the home plate when it lands as the parabola is a symmetric figure and the vertical line through the vertex is the axis of symmetry.

Let the equation of the path of the baseball be y = a(x-50)²+60. Since the point (0,0) is on this path, on substituting x = 0 and y = 0 in this equation, we get 2500a +60 = 0 so that a = -60/2500 = -6/250. Thus, the equation of the path of the baseball is y = (-6/250) (x-50)²+60.