# How do you find the amplitude, period, and shift for y = 2sin (2x - pi) +1?

Jun 1, 2016

$2 , \pi , - \pi$

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{sine wave function}}$ is

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

where amplitude = |a| , period$= \frac{2 \pi}{b}$ , c is the phase shift and
d, the vertical shift.

here amplitude = |2| = 2 , period$= \frac{2 \pi}{2} = \pi$

phase shift $= - \pi \text{ and vertical shift } = \left(\begin{matrix}0 \\ 1\end{matrix}\right)$