Question

Write up the specifics of your design so that the advertising department’s art team can create a finalized version. You should include the equations you used in your design, along with any domain restrictions or important intersection points. You should also include relevant information about colors. Finally, write a short pitch (3 sentences) about why your logo is the best choice for your company and why you think it will appeal to buyers.
short no points and at a 6th grade level

Answer 1

Design summary for final art (vector file): Use two equal circles of radius 4 units centered at (-1.5, 0) and (1.5, 0). Their equations are (x + 1.5)^2 + y^2 = 16 and (x − 1.5)^2 + y^2 = 16. Add a small inner circle centered at (0, 0) with radius 1.2: x^2 + y^2 = 1.44. Add a vertical stem as a rectangle centered on x = 0, with width 0.6 and running from y = −4.5 down to y = −6 (so the stem sits below the two-circle shape).

Domain restrictions and intersections: The two large circles intersect at x = 0 and y = ±sqrt(16 − 1.5^2) = ±sqrt(13.75) ≈ ±3.708, so the overlap points are (0, 3.708) and (0, −3.708). The small inner circle is fully inside the overlap area and does not intersect the big circles. The stem is the rectangle x ∈ [−0.3, 0.3], y ∈ [−6, −4.5].

Rendering and color guides: Fill the left big circle with teal #006D77 (RGB 0,109,119) and the right big circle with bright turquoise #00B4D8 (RGB 0,180,216). Use a horizontal linear blend in the overlap so the center area reads as a lighter mix; place the small inner circle in warm yellow #FFD166 (RGB 255,209,102) to make a friendly focal point. Stroke all outer shapes with dark charcoal #222222 (RGB 34,34,34) at 2–3 px for crisp edges. Export as vector (SVG/AI/PDF) and provide a version at 1000 px width for web and a CMYK conversion for print.

Pitch (3 sentences): This logo is simple, clean, and easy to remember. The two rounded shapes and bright center feel friendly and professional. Buyers will like the calm teal colors with a warm pop that stands out.