ANSWER
The first graph.
Step-by-step explanation
We want to identify the correctly sketched graph for the scenario given.
The graph is to represent the motion of the ball as it is thrown in the air. This means that the graph must open downward since its vertex must be a maximum.
The ball is at a height of 4 feet when it leaves the hand of the thrower. This means that when the time is 0 seconds, the ball is at 4 feet. This signifies the y-intercept of the graph.
In other words, the y-intercept of the graph is 4 ft.
The maximum height reached by the ball is 6.25 feet and this occurs after 1.5 seconds. This represents the maximum of the graph i.e. the vertex of the graph.
In other words, the vertex of the graph is at (1.5, 6.25)
Therefore, we see that the graph that correctly contains the correct information is the first graph. That is the answer.