Final Answer:
The graph and table provide representations of the height of Carla and Rachel's baseballs over time, while Jack's baseball height is expressed by the quadratic function h(t) = -t² + 5t + 6.
Step-by-step explanation:
Carla's baseball height is depicted in the graph, where the vertical axis denotes the height in feet, and the horizontal axis represents time in seconds. The curve on the graph illustrates how the height changes with time.
Rachel's recorded height of her baseball at each second is provided in the table. The table likely shows the time (in seconds) in the first column and the corresponding height (in feet) in the second column. Analyzing the table allows for a detailed understanding of Rachel's baseball's height trajectory.
As for Jack's baseball, its height is expressed by the quadratic function h(t) = -t² + 5t + 6. This equation represents a downward-opening parabola, where 't' is the time in seconds, and 'h(t)' is the height in feet. The maximum height occurs at the vertex of the parabola, which can be calculated using the formula
![\[ t = (-b)/(2a) \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/4k3175oene3fxj9fpc3c6ukidujgo2ik4e.png)
where 'a' is the coefficient of the squared term, 'b' is the coefficient of the linear term, and 'c' is the constant term. The vertex provides information about the maximum height Jack's baseball reaches during its flight.
Understanding the graphical and numerical representations of Carla and Rachel's baseballs, along with the mathematical expression for Jack's baseball, allows for a comprehensive analysis of their respective heights over time.