Design a wine glass that uses at least 5 different equations to form the outline of the shape. At least half of your equations must be curves. It is easier if the design is done with the glass on its side, that is, with the axis of the design running along the x-axis

To design a wine glass using equations, we can use a combination of linear equations and quadratic equations to create curves. Let's start by breaking down the overall shape of the wine glass into different sections.

1. Base of the glass:
For the base of the glass, we can use a simple equation for a straight line. Let's say we want the base to have a width of 4 units, centered at the origin (0,0). An equation for the base could be:
y = 2 (where x ranges from -2 to 2)

2. Curved section:
To create the curved section of the glass, we can use a quadratic equation to form a curve. Let's use a parabola with its vertex at the origin (0,0). An equation for the curve could be:
y = x^2

3. Stem of the glass:
For the stem of the glass, let's use a pair of curves that resemble a slender elliptical shape. Here are two equations that can be used:

Upper curve:
y = sqrt(4 - x^2) + 4

Lower curve:
y = -sqrt(4 - x^2) + 1

These equations represent an ellipse with a vertical axis of length 4 and centered at (0,4).

4. Rim of the glass:
To create the rim of the wine glass, we can use a simple linear equation. Let's use a straight line equation tilted slightly downwards. An equation for the rim could be:
y = -0.2x + 4.5

By using these equations, we have created a design for a wine glass with a base, a curved section, a stem, and a rim. These equations provide the outline of the glass when the glass is viewed from the side, with the x-axis as the axis of the design. You can plot these equations on a graphing software or program to visualize the design.