Question

You are attending a baseball game. The batter hits the ball high into the air of the infield. You notice the ball, as it is hit, forms a parabolic path from contact with the bat to where it lands in the field. The path the ball traveled can be expressed by the quadratic equation
У =-1/24 x2
+ 2x, where x represents the horizontal distance and y represents the height of the ball. Interpret the following key feature of the parabola in terms of the context. (1 point)
Range: 0 ≤

Answer 1

The given quadratic equation \( y = -\frac{1}{24}x^2 + 2x \) describes the path of the baseball as it is hit into the air. In this context:

- \( x \) represents the horizontal distance from the point where the ball is hit.
- \( y \) represents the height of the ball above the ground.

When we analyze the range \( 0 ≤ y \), we interpret this in terms of the baseball game:

- The condition \( 0 ≤ y \) indicates that the height of the baseball (y) cannot be negative. This makes sense because the height of the ball above the ground cannot be below ground level; it must be zero or more.
- Therefore, the range of the quadratic function confirms that the ball will be at least at ground level and can rise to a certain maximum height (which can be determined later) before coming back down, at which point it will eventually land back on the ground.

In summary, the range \( 0 ≤ y \) implies that the baseball is always above or at ground level throughout its parabolic flight path.