You are attending a professional baseball game. The batter hits the ball into right field. You notice the ball, as it is hit, forms a parabolic path from the bat to where it lands in the field. The path the ball traveled can be expressed by the quadratic equation y=−142(x−50)2+60

Question

You are attending a professional baseball game. The batter hits the ball into right field. You notice the ball, as it is hit, forms a parabolic path from the bat to where it lands in the field. The path the ball traveled can be expressed by the quadratic equation  y=−142(x−50)2+60
 ,  where x is the distance from home plate, and y is the height in the air as the ball travels in the air. Interpret the following key feature of the parabola in terms of the context.

GPT 3.5 · Answer

The key feature of the parabola is the vertex, which in this case is at the point (50,60). This means that the highest point the ball reached in its trajectory was 60 feet in the air, and this height occurred at a distance of 50 feet from home plate. This tells us that the ball achieved its maximum height at the halfway point between home plate and where it ultimately landed in right field.