A diver's depth below the surface of the water, in meters, is modeled by a quadratic function $D(t)$, where $t$ is the time in minutes after entering the water. The diver reaches a maximum depth of $20$ meters $3$ minutes after entering the water and then resurfaces $6$ minutes after entering the water. Based on this function, what was the estimated depth, in meters, of the diver $1$ minute after entering the water?