How do I find the amplitude, period, horizontal shift and vertical shift for the graph of y=3sin2(θ-30)+1?

horizontal shift is leftward 30

vertical shift is up 1

period is pi , from 2pi / the 2 after the sin function The horizontal line about which this wave oscillates is shifted 1 up, The amplitude is 3 above and below the shifted horizntal axis Horizontal shift is -pi

Start with y = sinθ

θ --> 2θ so original period is halved to pi

y --> y/3

y = 3sin2θ so original amplitude becomes 3 times

θ --> θ - 30

y = 3sin2(θ-30) so orig graph's shifted to the right by 30

y --> y - 1

y = 3sin2(θ-30) + 1 so original graph's shifted up by 1

amplitude 3 (like you guessed),

period pi,

horizontal shift +30

vertical shift +1