1. The problem asks us to draw a wave with an amplitude of 2 and a wavelength of 4 by plotting points and connecting them smoothly. 2. The amplitude is the maximum displacement from the center line (y=0), which is 2 here. 3. The wavelength is the distance over which the wave pattern repeats, which is 4 units along the x-axis. 4. The given points are (1,2), (2,0), (3,-2), and (4,0). These points represent one full wave cycle: peak at (1,2), crossing zero at (2,0), trough at (3,-2), and crossing zero again at (4,0). 5. To continue the wave, repeat this pattern every 4 units along the x-axis. So the next points would be (5,2), (6,0), (7,-2), (8,0), and so on. 6. Connecting these points with a smooth, curved line forms a sinusoidal wave with amplitude 2 and wavelength 4. 7. The wave equation that fits this pattern is $$y=2\sin\left(\frac{2\pi}{4}x\right)=2\sin\left(\frac{\pi}{2}x\right)$$. 8. This equation produces peaks at $x=1,5,9,...$ and troughs at $x=3,7,11,...$, matching the plotted points. 9. Thus, the wave with amplitude 2 and wavelength 4 is correctly represented by the points and the sine function above. Final answer: The wave can be described by $$y=2\sin\left(\frac{\pi}{2}x\right)$$ and the plotted points form one cycle of this wave.