🧮 Graphing with Desmos - NagusameCS/IVY GitHub Wiki

⚠️ Desmos API Disclaimer ⚠️

NOTICE: Unauthorized use of the Desmos API in a production enviornment is strictly prohibited.

🔒 Use is Restricted

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violates Desmos’s policies and may result in service disruption, legal action, or blacklisting.

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⸻

If you’re unsure whether your use case is allowed, assume it is not. Always contact Desmos directly to clarify before integrating any of their services.

Learn more and request access at: https://www.desmos.com/partners

This guide explains how to use the Desmos graphing calculator integration in IVYSTUDY markdown files.

Basic Syntax

To create a Desmos graph, use a code block with the desmos identifier:

```desmos
y=x^2
```

Configuration Options

Setting Calculator Options

Use a config comment at the start of the code block:

```desmos
//config: {
  "bounds": {"x": [-10, 10], "y": [-10, 10]},
  "grid": true,
  "expressions": false
}
y=x^2
```

Common Configuration Properties

{
  "bounds": {"x": [min, max], "y": [min, max]}, // Set viewing window
  "grid": true/false,                           // Show/hide grid
  "expressions": true/false,                    // Show/hide expression list
  "expressionsCollapsed": true/false,          // Collapse expression list
  "lockViewport": true/false,                  // Prevent panning/zooming
  "showGrid": true/false,                      // Show/hide grid
  "showXAxis": true/false,                     // Show/hide x-axis
  "showYAxis": true/false,                     // Show/hide y-axis
  "xAxisLabel": "string",                      // Label for x-axis
  "yAxisLabel": "string"                       // Label for y-axis
}

Basic Examples

Simple Function

```desmos
y=x^2
```

Multiple Functions

```desmos
y=x^2
y=2x+1
y=sin(x)
```

Configured Graph

```desmos
//config: {
  "bounds": {"x": [-5, 5], "y": [-2, 8]},
  "grid": true,
  "expressions": true
}
y=x^2
y=2x+1
```

Advanced Features

Points and Lines

```desmos
//Points
(1,2)
(3,4)

//Line segment
(1,2)(3,4)

//Vector
vector(1,2)
```

Inequalities

```desmos
y>x^2
y<2x+1
```

Parametric Equations

```desmos
(cos(t), sin(t))
```

Polar Equations

```desmos
r=2cos(theta)
```

Interactive Elements

Sliders

```desmos
//Create a slider
a=1
y=ax^2
```

Points with Labels

```desmos
A=(1,2)
B=(3,4)
(A_x, A_y)
```

Advanced Applications

Function Family

```desmos
//config: {
  "bounds": {"x": [-5, 5], "y": [-5, 5]}
}
a=1
y=ax^2
y=(a+1)x^2
y=(a+2)x^2
```

Geometric Construction

```desmos
//Circle
(x-h)^2+(y-k)^2=r^2

//Points
A=(0,0)
B=(2,0)
C=(1,2)

//Triangle sides
segment(A,B)
segment(B,C)
segment(C,A)
```

Best Practices

  1. Configuration

    • Always set appropriate bounds for your graph
    • Consider whether expressions list should be visible
    • Use grid when it aids understanding

  2. Clarity

    • Use descriptive variable names
    • Add comments for complex constructions
    • Keep expressions organized

  3. Performance

    • Limit number of expressions for better performance
    • Avoid unnecessarily complex calculations
    • Use reasonable domains for functions

  4. Accessibility

    • Provide clear labels for axes when relevant
    • Use appropriate zoom levels
    • Consider color contrast for visibility

Common Use Cases

For Teaching Math

```desmos
//config: {
  "bounds": {"x": [-5, 5], "y": [-5, 5]},
  "expressions": true
}
// Parent function
y=x^2

// Transformed function
a=1 //vertical shift
h=0 //horizontal shift
y=(x-h)^2+a
```

For Physics Problems

```desmos
//config: {
  "bounds": {"x": [0, 10], "y": [0, 20]},
  "xAxisLabel": "Time (s)",
  "yAxisLabel": "Height (m)"
}
// Projectile motion
g=9.81
v_0=15
theta=45
y=(-g/2)x^2+v_0*sin(theta*pi/180)x
```
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