The equation of the parabola given is
Vertex
The vertex of a parabola expressed in the standard form
In this case:
Calculating the x-coordinate of the vertex:
To find the corresponding y-coordinate, substitute
Thus, the vertex of the parabola is at the point
Interpretation
The vertex
Intercepts
Next, we can also find the x-intercepts (where the ball hits the ground) by setting
This gives us one intercept at
Thus, the x-intercepts occur at
Summary
- Vertex: The maximum height of the ball is 24 units at a horizontal distance of 24 units from home plate. This indicates the peak of the ball's trajectory.
- Intercepts: The ball starts its path at
when it was hit and lands at units, showing how far the ball traveled before touching down.
These features help us understand the trajectory of the ball, including its highest point and the distance it traveled.