Answer
The amplitude of $ y=-4\cos \frac{\pi }{2}x $ is 4 and the period of $ y=-4\cos \frac{\pi }{2}x $ is 4.
Work Step by Step
Consider the given equation,
$ y=-4\cos \frac{\pi }{2}x $
The equation is of the form $ y=A\cos Bx $ with $ A=-4$ and $ B=\frac{\pi }{2}$.
Amplitude of $ y=-4\cos \frac{\pi }{2}x $ is given by $\left| A \right|=\left| -4 \right|=4$
Period of $ y=-4\cos \frac{\pi }{2}x $ is given by $\frac{2\pi }{B}=\frac{2\pi }{\frac{\pi }{2}}=2\pi \times \frac{2}{\pi }=4$
Thus, the amplitude of $ y=-4\cos \frac{\pi }{2}x $ is 4 and the period of $ y=-4\cos \frac{\pi }{2}x $ is 4.
Graph:
Step1: Identify the amplitude and the period of $ y=-4\cos \frac{\pi }{2}x $.
The amplitude of $ y=-4\cos \frac{\pi }{2}x $ is 4 means that the maximum value of $ y $ is 4 and the minimum is $-4$.
The period of $ y=-4\cos \frac{\pi }{2}x $ is 4 means that each cycle is of length of 4.
Step 2: Find the values of $ x $ for the first five key points. Begin by dividing the period 4, by 4.
$\frac{\text{period}}{4}=\frac{4}{4}=1$
Start with the value of $ x $ where the cycle begins, ${{x}_{1}}=0$. Adding quarter periods 1, the five key points are:
$\begin{align}
& {{x}_{1}}=0 \\
& {{x}_{2}}=0+1=1 \\
& {{x}_{3}}=1+1=2 \\
& {{x}_{4}}=2+1=3 \\
& {{x}_{5}}=3+1=4 \\
\end{align}$
