Given the slope m and a point (a,b) of a line, its equation is given by

In your case, a = -4, b = 7 and m=1/2, so we have

When we graph the function, it has a vertex of (3, 16).
The maximum of the graph is the highest "x" value on the graph which is 3.
Since the maximum is 3, it will take 3 seconds for the ball to reach its maximum height.
A graph will be shown below showing the function and vertex.
Best of Luck!