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y = -1/5 sin(4x + π)

What is the Amplitude?
Vertical shift?
Period?
Phrase shift?

that's "phase" not "phrase"

and recall that
a sin(b(x-c)) + d
has
amplitude = |a|
vertical shift up d
period 2π/b
phase shift right c
so now plug in your numbers

Did you know?

Did you know that in the equation y = -1/5 sin(4x + π), the amplitude is 1/5? The amplitude represents half the distance between the maximum and minimum values of the function, and in this case, it is positive since the negative sign only affects the sign of the function. Another interesting fact is that there is a vertical shift of 0 since there is no constant term added or subtracted to the function. The graph of the function will pass through the origin (0,0) without any vertical displacement. The period of the function, or the length of one complete cycle, can be determined by dividing 2π by the coefficient of x, which in this case is 4. Therefore, the period is π/2. It means that the graph will complete one full cycle from 0 to 2π in a span of π/2. Lastly, there is a phrase shift of π units to the left. The equation 4x + π implies that the entire function is horizontally shifted by π/4 units to the left. This means that the graph will begin at x = -π/4, where it reaches its maximum value, instead of starting from x = 0. Understanding the amplitude, vertical shift, period, and phrase shift of trigonometric functions can help in analyzing and graphing various mathematical functions.