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

Mar 28, 2018

As detailed below.

#### Explanation:

Standard form of equation $y = A \sin \left(B x - C\right) + D$, where

$A m p l i t u \mathrm{de} = | A | , \text{ Period " = (2pi)/|B|, " Phase shift " = (-C) / B, } V e r t i c a l S h \mathmr{if} t = D$

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

$A m p l i t u \mathrm{de} = | A | = 2$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{/} | - 2 | = \pi$

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

$\text{ Vertical Shift } = D = 1$

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