Question

What is the equation of the following graph?

Answer 1

Explanation:

When figuring out the graph of a sinusoidal, I keep in mind the acronym FPARHM:

F - function (sine or cosine)

P - period

A - amplitude

R - reflections

H - horizontal/phase shift

M - midline

Looking at the graph, we can figure out that the function is sine (since it intersects the origin at its midpoint, the period is
`\pi` (because it repeats every
`/pi` units in the x-direction, the amplitude is 2 (because the graph's extreme points are 2 units away from the midline in the y-direction, there are no reflections, no horizontal/phase shift, and the midline is
`y=0` (since the graph isn't shifted up or down in the y-direction.

Finally, knowing all these parts, we can piece together the equation of the sinusoidal graph. In general, the equations of sinusoidal graphs are in the form
`y=a\sin(bx+c)+d` where
`|a|` is the amplitude,
`(2\pi)/(|b|)` is the period,
`(c)/(b)` is the horizontal shift, and
`d` is the midline. Additionally, if
`a` is negative, the graph needs to be reflected over the x-axis and if
`b` is negative, the graph needs to be reflected over the y-axis. Knowing this, all we need to do is plug in the amplitude, period, phase shift, and midline to the equation. The equation is
`y=2\sin(2x)`

Hope this helps :)