# How do you determine the amplitude, period, and shifts to graph y=-sinx+2?

Jun 3, 2016

$1 , 2 \pi , \text{vertical shift of} + 2$

#### 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 horizontal shift and d , the vertical shift

here a = -1 , b = 1 , c = 0 and d = 2

hence amplitude = |-1| = 1 , period$= \frac{2 \pi}{1} = 2 \pi$

there is no horizontal shift and vertical shift of $\left(\begin{matrix}0 \\ 2\end{matrix}\right)$