Analyze \(y~=~2\cos(3x)~-~1\). State \(A\), \(B\), \(h\), and \(D\); give the amplitude, reflection, period, phase shift, midline, range, and quarter-period; and list the \(\text{five}~\text{ordered}~\text{anchors}\) for one cycle with their direction or extrema.

Compute the cosine cycle’s vertical geometry from the midline and amplitude, and its horizontal geometry from the period and quarter-period. The starting pattern matters: with a positive coefficient, cosine begins at a maximum rather than on the midline. Advancing by equal quarter-period steps should produce maximum, midline falling, minimum, midline rising, and maximum again.