1. The problem is to understand the shape of the moon during its first or last quarter phase, which resembles a crescent shape. 2. The crescent moon shape can be modeled mathematically using the intersection of two circles or by using specific functions that create a curved shape pointed at each end. 3. One common way to represent a crescent shape is by subtracting one circle from another overlapping circle, but for graphing purposes, a simple function that resembles a crescent can be given by: $$y = \sqrt{1 - x^2} - 0.5\sqrt{1 - (x - 0.5)^2}$$ 4. This function represents the upper semicircle of radius 1 centered at the origin minus a smaller semicircle of radius 0.5 shifted to the right by 0.5 units, creating a crescent shape. 5. The crescent is pointed at each end because the difference of the two semicircles creates two points where the curves meet. 6. This matches the description of the moon in its first or last quarter phase, where the visible part is a curved shape pointed at each end, known as a crescent. Final answer: The crescent moon shape can be modeled by the function $$y = \sqrt{1 - x^2} - 0.5\sqrt{1 - (x - 0.5)^2}$$ which produces a curved shape pointed at each end, representing the crescent moon phase.