Fun Things to Put in Desmos Graphing Calculator

The Desmos graphing calculator is more than just a tool for plotting functions - it's a creative playground for exploring mathematics visually. Whether you're a student learning concepts or an educator demonstrating ideas, Desmos offers endless possibilities for fun and educational graphing experiments.

Basic Graphs to Try

Start with simple functions to get comfortable with Desmos' interface. These basic graphs help you understand how the calculator works before moving to more complex concepts.

1. Quadratic Functions

Graph y = x² to see the classic parabola. Try variations like y = 2x², y = -x² + 3, or y = (x-1)² + 2 to explore how coefficients and transformations affect the graph.

General form: y = ax² + bx + c

Where a determines the parabola's width and direction, b affects the tilt, and c shifts the vertex.

2. Absolute Value Graphs

Enter y = |x| to see the V-shape. Experiment with y = |x-2| + 1 to see how transformations work with absolute value functions.

3. Trigonometric Functions

Graph y = sin(x) and y = cos(x) to visualize the sine and cosine waves. Try combining them with y = sin(x) + cos(x) to see how they interact.

Tip: Use the slider feature in Desmos to create interactive graphs where you can adjust parameters with a simple drag.

Parametric Equations

Parametric equations let you define both x and y in terms of a third variable, t. This opens up new possibilities for creating complex shapes.

1. Lissajous Curves

Enter x = sin(2t) and y = sin(3t) to create a beautiful Lissajous curve. Change the coefficients to see different patterns emerge.

2. Heart Shape

Use the parametric equations:

x = 16sin³(t)

y = 13cos(t) - 5cos(2t) - 2cos(3t) - cos(4t)

This creates a classic heart shape that's a great example of how parametric equations can create complex forms.

Polar Coordinates

Polar coordinates express points as a distance from the origin and an angle, creating circular and spiral patterns.

1. Flower Patterns

Graph r = sin(5θ) to create a five-petal flower. Change the coefficient to create flowers with different numbers of petals.

2. Spiral Galaxies

Enter r = θ to create an Archimedean spiral. Try r = e^(θ/10) for an exponential spiral.

Note: Polar graphs in Desmos use r for radius and θ for angle, following standard mathematical notation.

3D Graphs

Desmos supports 3D graphing, allowing you to visualize surfaces and volumes in three dimensions.

1. Saddle Surface

Graph z = x² - y² to see the classic saddle-shaped surface. This is a fundamental example in calculus.

2. Wave Patterns

Enter z = sin(x)cos(y) to create a wave pattern that's useful for understanding wave interference.

3. Parametric Surfaces

Use parametric equations to create complex surfaces. For example:

x = u

y = v

z = sin(u)cos(v)

This creates a wave-like surface that demonstrates how parametric equations can model real-world phenomena.

Interactive Examples

Desmos shines when you create interactive graphs that respond to user input. These examples show how to make your graphs more engaging.

1. Interactive Parabola

Create a slider for 'a' in the equation y = a(x-h)² + k. Users can drag the slider to see how changing the coefficient affects the parabola's shape.

2. Projectile Motion Simulator

Use parametric equations with sliders for initial velocity and angle to simulate projectile motion. This helps visualize how these factors affect a projectile's path.

3. Population Growth Model

Graph y = P₀e^(rt) with sliders for initial population (P₀) and growth rate (r). This demonstrates exponential growth in a visual way.

Tip: Use Desmos' "Add Slider" feature to create interactive elements that users can adjust with a simple drag.

FAQ

Can I save my Desmos graphs for later use?: Yes, Desmos automatically saves your work in the cloud. You can access your saved graphs from any device by signing in to your Desmos account.
Is Desmos free to use?: Yes, Desmos offers a free version with all the basic graphing features. There's also a paid Pro version with additional features like offline access and advanced sharing options.
Can I use Desmos for educational purposes?: Absolutely! Desmos is widely used in schools and universities for teaching mathematics. Its interactive features make it particularly effective for demonstrating concepts.
What's the difference between Desmos and other graphing calculators?: Desmos stands out for its user-friendly interface, powerful features, and focus on interactivity. It's particularly strong at visualizing complex functions and creating interactive models.
Can I export my Desmos graphs as images or PDFs?: Yes, Desmos allows you to export your graphs as PNG images or PDF documents. You can find these options in the "Download" menu.