Answer
The Amplitude is $ 0.5$
The Period is $ \pi $
The Horizontal shift is $\frac {\pi}{6}$ units to the right
See graph below.
Work Step by Step
For $y=a\sin c(x−h) + k$ $y =a \cos c(x−h) + k$,
Amplitude: $|a|$, Period: $\frac{2\pi} {|c|}$,
Horizontal Shift: h
The question asks for a graph, amplitude, period, and horizontal shift of the function.
Given $y = -0.5 \cos (2x - \frac{\pi}{3}) + 0.5$
$y = -0.5\cos 2(x - \frac{\pi}{6}) + 0.5 $
The Amplitude is $|-0.5| = 0.5$
The Period is $\frac{2\pi}{|2|} = \pi $
The Horizontal shift is $\frac {\pi}{6}$ units to the right
See graph below.