Question

Identify the amplitude, period and vertical shift shown in the graph. Then use that information to write an equation for the sine function shown.Use the formula keypad when necessary.(2 points)

Answer 1

I don't see the graph — could you upload it or give the key values (max, min, and one or two x-coordinates of successive peaks/troughs or zero crossings)? With that I can give the specific numbers and the equation.

Meanwhile, here are the exact steps you can use to read the graph and write the sine equation:

1. Identify max and min values from the graph:
- Amplitude A = (max − min)/2
- Vertical shift (midline) D = (max + min)/2

2. Find the period:
- Measure the horizontal distance between two consecutive peaks (or two consecutive troughs or two consecutive identical zero crossings). That distance = period P.
- Then B = 2π / P (if you want the function in radians). If the graph uses degrees, B = 360°/P.

3. Choose the phase shift C:
- Standard sine y = A sin(B(x − C)) + D has a midline crossing going upward at x = C.
- Locate an x-value x0 on the graph where the curve crosses the midline going upward (or use a peak location and adjust by P/4: a peak occurs at C + P/4).
- Then C = x0 (if x0 is that upward midline crossing). If you used a peak at xpeak, then C = xpeak − P/4.

4. Write the equation:
- y = A sin(B(x − C)) + D
- If the graph is reflected (starts downward) use a negative amplitude: y = −A sin(B(x − C)) + D, or equivalently shift C by P/2.

5. If you have one point (x1,y1) and you know A, B, D, you can solve C:
- y1 = A sin(B(x1 − C)) + D => sin(B(x1 − C)) = (y1 − D)/A
- Then B(x1 − C) = arcsin((y1 − D)/A) + 2πk, solve for C and pick the value matching the graph.

If you upload the graph or give max, min, and a horizontal spacing between peaks (or coordinates for two notable points), I will compute amplitude, period, vertical shift and give the final sine equation.