Answer
$Amplitude = 3 $
$Period = 2$
$Horizontal\ shift$ = right shift $\frac{1}{4}$
$Vertical\ shift$ = $\frac{5}{2}$ upward shift
Work Step by Step
If C is any real number and $B> 0$, then the graphs of $y = k + A\sin(Bx+C)$ and $y = k + A\cos (Bx+C)$ will have
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Vertical\ shift = k$
so for $y = \frac{5}{2} -3\cos (\pi x - \frac{\pi}{4} )$
$Amplitude = |-3| = 3 $
$Period = \frac{2\pi}{\pi} = 2$
$Horizontal\ shift = (–\frac{-\frac{\pi}{4}}{\pi}) = \frac{1}{4}$ i.e right shift $\frac{1}{4}$
$Vertical\ shift = \frac{5}{2}$ ($\frac{5}{2}$ upward shift)