1. The user requests to graph the given functions and the circle equation. 2. The functions are: - Supply function 1: $Q = 2P - 1$ - Demand function: $Q = 20 - 2P$ - Supply function 2: $Q = -4 + 3P$ - Parabola 1: $Y = 2X^2 - 8X + 5$ - Parabola 2: $Y = -5X^2 + 30X - 35$ - Circle: $-3X^2 - 3Y^2 - 24X + 12Y - 60 = 0$ 3. For graphing, we rewrite the circle equation in standard form: Divide entire equation by $-3$: $$X^2 + Y^2 + 8X - 4Y + 20 = 0$$ Complete the square for $X$ and $Y$: $$X^2 + 8X + Y^2 - 4Y = -20$$ Add $(\frac{8}{2})^2 = 16$ and $(\frac{-4}{2})^2 = 4$ to both sides: $$X^2 + 8X + 16 + Y^2 - 4Y + 4 = -20 + 16 + 4$$ Simplify: $$(X + 4)^2 + (Y - 2)^2 = 0$$ This represents a circle with center $(-4, 2)$ and radius $0$, which is a single point. 4. The Desmos-compatible functions for graphing are: - $y = 2x - 1$ - $y = 20 - 2x$ - $y = -4 + 3x$ - $y = 2x^2 - 8x + 5$ - $y = -5x^2 + 30x - 35$ 5. The circle is a point at $(-4, 2)$. 6. These can be graphed to visualize the supply and demand lines, parabolas, and the degenerate circle. Final answer: Graph the functions $y = 2x - 1$, $y = 20 - 2x$, $y = -4 + 3x$, $y = 2x^2 - 8x + 5$, $y = -5x^2 + 30x - 35$, and plot the point $(-4, 2)$ for the circle.