1. **State the problem:** We need to graph a sine function with amplitude 4, period $\pi$, midline $y=-3$, and y-intercept at $(0,-3)$. The graph is not reflected over the x-axis. 2. **Recall the general sine function formula:** $$y = A \sin(B(x - C)) + D$$ where: - $A$ is the amplitude, - $\frac{2\pi}{B}$ is the period, - $C$ is the horizontal shift, - $D$ is the vertical shift (midline). 3. **Identify parameters:** - Amplitude $A = 4$ - Period $\pi = \frac{2\pi}{B} \Rightarrow B = \frac{2\pi}{\pi} = 2$ - Midline $D = -3$ - Since the y-intercept is at $(0,-3)$, which is on the midline, and the graph is not reflected, the sine function starts at the midline going upward. 4. **Write the function:** $$y = 4 \sin(2x) - 3$$ 5. **Check the first two points:** - At $x=0$, $y = 4 \sin(0) - 3 = -3$ (midline), matches the y-intercept. - The next point is a maximum or minimum closest to $x=0$. 6. **Find the maximum point:** The sine function reaches maximum at $\sin(\frac{\pi}{2})=1$, so solve for $x$: $$2x = \frac{\pi}{2} \Rightarrow x = \frac{\pi}{4}$$ At $x=\frac{\pi}{4}$: $$y = 4 \times 1 - 3 = 1$$ 7. **Summary:** - First point: $(0,-3)$ on midline - Second point: $(\frac{\pi}{4},1)$ maximum This matches the problem requirements. **Final function:** $$y = 4 \sin(2x) - 3$$