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Can you help me solve please!!

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2sin((1)x + 135)-3

Step-by-step explanation:

Asin(Bx+C)+D

A = amplitude = distance from top to bottom divided by 2

y value of top = -1

y value of bottom = -5

distance from top to bottom = -1 - (-5) = 4

divide by 2 to get 4/2 = 2 as our amplitude

2π/B = period

in this case, we're working in degrees for our x axis - 2π = 360°

thus, 360°/B = period

period = time it takes to get from one high to the next (alternatively, one low to the next etc.) = 360 degrees in this case

thus, 360°/B = 360°

divide both sides by 360° and multiply both sides by B to isolate B

360/360 = B = 1

phase shift = -C/B

phase shift refers to how much the graph is shifted to the left/right. normally, the middle of a sin wave is at 0, with a peak being to the right of it. now, the middle of the sin wave (which has a peak to the right of it) is at x = -135 degrees to the right of a regular sine wave

thus,

-135 degrees = -C/B

B = 1

-135 degrees = -C

C = 135 degrees

D = vertical shift

the center is now at y = -3. normally, the center is at y = 0. thus, D = -3

our formula is thus

2sin((1)x + 135)-3
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