<image>The isosceles trapezoid \(ABCD\) is shown in the figure, with its base \(AD\) on the \(x\)-axis and vertex \(C\) on the positive half of the \(y\)-axis. Point \(B\) is at \((4, 2)\). The linear function \(y = kx - 1\) bisects its area. The graph of the function \(y = mx^{2} - (3m + k)x + 2m + k\) in terms of \(x\) has only two intersection points with the coordinate axes. Determine the value of \(m\). 