# How do you find the amplitude, period, and shift for f(x) = -4 cos(3x - π) + 1?

Mar 14, 2018

$4 , \frac{2 \pi}{3} , \frac{\pi}{3} , 1$

#### Explanation:

$\text{the standard form of the cosine is}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a \cos \left(b x + c\right) + d} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where amplitude "=|a|," period } = \frac{2 \pi}{b}$

$\text{phase shift "=-c/b," vertical shift } = d$

$\text{here "a=-4,b=3,c=-pi" and } d = 1$

$\Rightarrow \text{amplitude "=|-4|=4," period } = \frac{2 \pi}{3}$

$\text{phase shift "=-(-pi)/3=pi/3," vertical shift } = + 1$