Question

Use the image to answer the question.

A waveform is graphed on a coordinate plane.

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 can do that, but I don't have the image. Please either upload the graph image or tell me the key coordinates (y-values of a maximum and a minimum, and the x-distance for one full cycle or the x-coordinates of two successive identical points such as two consecutive peaks).

How to get the values from the graph (so you can tell me or I can compute when I see the image):

- Amplitude A = (maximum y − minimum y) / 2.
- Vertical shift D (midline) = (maximum y + minimum y) / 2.
- Period T = horizontal distance for one full cycle (e.g., x₂ − x₁ for two consecutive peaks).
- Angular frequency B = 2π / T.
- Phase shift C: pick a reference point (commonly the x for a midline crossing going upward or the first peak) and solve for C in y = A sin(B(x − C)) + D.

Example (so you know the final form): if max = 3 and min = −1 then A = 2, D = 1. If one period spans 4 units, B = 2π/4 = π/2. If the midline crossing going upward is at x = 1 then C = 1, so the equation is y = 2 sin((π/2)(x − 1)) + 1.

Upload the graph or provide the numeric values and I’ll compute the exact equation.