Problem

Analyze \(y~=~4\sin(x/2)~-~2\). 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.

Prompt coordinate grid scaled for one cycle of the stated trigonometric equation; the curve and derived features are withheld.

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Parameters: A = 4, B = 1/2, h = 0, D = −2; amplitude 4; no reflection.
Cycle: period 4π; shift 0; midline y = −2; range [−6, 2]; quarter-period π.
Anchors: (0, −2) rising, (π, 2) maximum, (2π, −2) falling, (3π, −6) minimum, (4π, −2) rising.

Parameters: A = 4, B = 1/2, h = 0, D = −2; amplitude 4; no reflection.
Cycle: period 4π; shift 0; midline y = −2; range [−6, 2]; anchor spacing 4π.
Anchors: (0, −2) rising, (4π, 2) maximum, (8π, −2) falling, (12π, −6) minimum, (16π, −2) rising.

Parameters: A = −4, B = 1/2, h = 0, D = −2; amplitude −4; no reflection.
Cycle: period 4π; shift 0; midline y = −2; range [−6, 2]; quarter-period π.
Anchors: (0, −2) rising, (π, 2) maximum, (2π, −2) falling, (3π, −6) minimum, (4π, −2) rising.

Parameters: A = 4, B = 1/2, h = 0, D = −2; amplitude 4; no reflection.
Cycle: period π; shift 0; midline y = −2; range [−6, 2]; quarter-period π/4.
Anchors: (0, −2) rising, (π/4, 2) maximum, (π/2, −2) falling, (3π/4, −6) minimum, (π, −2) rising.

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Analyze \(y~=~4\sin(x/2)~-~2\). 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.

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