A ball is thrown from 4 feet off the ground with a vertical velocity of 30 feet per second. Is the ball at its maximum height after 1 second? In two or more complete sentences, explain how you know whether or not the ball is at its maximum height.

At maximum height, the velocity of the ball is zero. In other words, the ball is momentarily at rest at maximum height before  it starts falling down.
The following equation explains this scenario:

v=u-gt, but v = 0
Therefore,
0=u-gt => u = gt, u = 30 ft/s, g = 9.81 m/s^2 = 32.174 ft/s^2

Substituting;
t = u/g = 30/32.172 = 0.9324 seconds ≈ 1 second