Answer: [tex]\bold{B)\quad y=2\ sin2x+\dfrac{\pi}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the given graph,
- A (amplitude) = 2
- Phase Shift [tex]\bigg(\dfrac{C}{B}\bigg)[/tex] = [tex]\dfrac{\pi}{2}[/tex] to the left
- P (period) = π --> B = 2
Option B shows the value of D as [tex]\dfrac{\pi}{2}[/tex], which is incorrect since there is no vertical shift up. If the parenthesis included that value, like Option C, then it would have been correct.
