Question

13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.

amplitude: 4, period 4 phase shift = vertical shift = -2

Answer 1

Answer:

$y=4sin(\frac{\pi}{2} x+\pi)-2$

Step-by-step explanation:

The equation of a periodic  function is in the form:

y = Asin(Bx + C) + D

Where A = amplitude, B = 2π / period, D = vertical shift, phase shift = -C / B.

Given that:

amplitude: 4, period 4 phase shift = vertical shift = -2

Hence:

A = amplitude = 4, B = 2π / period = 2π / 4 = π / 2, D = vertical shift = -2.

Phase shift = -C / B

C = -phase shift * B = - * -2 * π / 2 = π.

Therefore substituting gives:

$y=4sin(\frac{\pi}{2} x+\pi)-2$