How do you use the amplitude and period to graph #y= 2 sin (-2x+pi) +1#?

1 Answer
Mar 28, 2018

Answer:

As detailed below.

Explanation:

Standard form of equation #y = A sin(Bx - C) + D#, where

#Amplitude = |A| , " Period " = (2pi)/|B|, " Phase shift " = (-C) / B, " Vertical Shift = D#

Given equation is y = 2 sin (-2x + pi) + 1#

#Amplitude = |A| = 2#

#"Period " = (2pi)/ |B| = (2pi)/ /|- 2| = pi#

#"Phase Shift " = (-C) / B = -pi / -2 = pi/2, " " (color(green)(pi/2 " to the right"))#

#" Vertical Shift " = D = 1#

graph{-2sin(2x-pi) + 1 [-10.125, 9.875, -4.84, 5.16]}