GeoGebra Guide for the IB Maths IA
Plot functions, fit curves to data, explore parameters with sliders, and export publication-quality graphs.
The Interface & Plotting Functions
1 Entering Functions
Type directly into the Input Bar at the bottom of the screen (Classic) or the entry field on the left (Graphing). GeoGebra uses standard mathematical notation - the table below covers the most common IA inputs.
| What you want | Type in GeoGebra |
|---|---|
| Quadratic y = 2x² − 3x + 1 | f(x) = 2x^2 - 3x + 1 |
| Exponential y = 3e^(0.4x) | f(x) = 3 * e^(0.4x) |
| Natural log y = ln(x) | f(x) = ln(x) |
| Trig function y = 2sin(3x) | f(x) = 2sin(3x) |
| Logistic curve | f(x) = L / (1 + e^(-k*(x - x0))) |
| Piecewise function | f(x) = If(x < 2, x^2, 2x - 1) |
| Parametric curve | Curve(cos(t), sin(t), t, 0, 2pi) |
| Derivative of f | f'(x) or Derivative(f) |
| Integral from a to b | Integral(f, a, b) |
| Vertical asymptote at x = 2 | x = 2 |
f(x) = ... rather than just the expression. This lets you reference the function later (e.g. f'(x) for the derivative, or f(3) to evaluate at a point) and labels it cleanly in the legend.
2 Customising Graph Appearance
Right-click any object in GeoGebra → Object Properties (or click the coloured dot next to it in the Algebra panel) to change colour, line thickness, line style, and label. For IA graphs:
Right-click the graphics area → Graphics Settings → set axis labels with units (e.g. "Time (s)", "Temperature (°C)"). Tick "Show axes" and set a sensible scale using the xMin, xMax fields. Hide unnecessary gridlines for a clean look.
Insert a text label: type Text("My graph title") in the input bar, then drag it into position. Alternatively, add the title in your IA document below the exported image as a proper figure caption - this is cleaner for word-processed submissions.
Use Root(f) to find x-intercepts, Extremum(f) for turning points, and Intersect(f, g) for intersection points. These create labelled points on the graph automatically - copy the coordinates into your IA working.
Menu → Download as → PNG. Set resolution to at least 300 dpi for print quality. Alternatively, use Share → Export Image in the browser version. Paste the PNG into your document and add a figure number and caption below.
Sliders & Parameter Exploration
Sliders let you vary a parameter interactively and see how the function changes - a powerful tool for the Reflection criterion, where you discuss the effect of changing model assumptions.
1 Creating a Slider
Type just a = 1 and press Enter. GeoGebra creates a slider for a automatically with a default range. The slider appears in the graphics view.
Right-click the slider → Object Properties → Slider tab. Set Min, Max, and Increment to values appropriate for your model. For a growth rate parameter you might use min = 0, max = 2, increment = 0.01.
Now type f(x) = a * e^(b*x) (creating a second slider b the same way). Drag the sliders to explore how each parameter affects the curve shape.
Take screenshots at two or three distinct parameter values. In your write-up, explain what each parameter controls mathematically: "Increasing a stretches the curve vertically, raising the initial value. Increasing b steepens the growth rate, as b is the coefficient in the exponent."
Regression & Data Fitting
GeoGebra can fit regression curves directly to a dataset - useful if you want a visual fit alongside the algebraic one you calculate in Sheets.
1 Entering a Dataset and Fitting a Curve
In the input bar, type: L = {(1, 3.2), (2, 5.1), (3, 8.4), (4, 13.9)} (replace with your actual values). GeoGebra plots all points instantly.
Use one of GeoGebra's built-in fit commands on your list L:
FitLine(L) - least-squares linear
FitPoly(L, 2) - quadratic (degree 2)
FitPoly(L, 3) - cubic
FitExp(L) - exponential y = ae^(bx)
FitLog(L) - logarithmic
FitPow(L) - power y = ax^b
FitLogistic(L) - logistic (S-curve)
The fitted curve appears on the graph and its equation shows in the Algebra panel on the left. Copy the exact coefficients into your IA - these are full-precision values, not the rounded ones shown on chart labels.
GeoGebra doesn't display R² automatically for all fit types. Calculate it in Sheets using =RSQ() on the same data, or type in GeoGebra: RSquare(L, f) where f is your fitted function name.
Calculus & Geometry Tools
1 Calculus in GeoGebra
| Operation | GeoGebra input | What it produces |
|---|---|---|
| Derivative | f'(x) or Derivative(f) | Plots f′(x) as a new function |
| Second derivative | f''(x) | Plots f″(x) |
| Definite integral | Integral(f, 1, 4) | Shades the area and returns the value |
| Turning points | Extremum(f, -5, 5) | Plots labelled local maxima/minima |
| Inflection points | InflectionPoint(f) | Plots labelled inflection points |
| Tangent at x = a | Tangent(a, f) | Draws the tangent line at that point |
| Normal at x = a | PerpendicularLine((a, f(a)), f) | Draws the normal line |
2 3D Geometry (GeoGebra 3D)
Go to geogebra.org/3d for the 3D app. This is useful for IAs involving volumes of revolution, 3D vectors, or geometric solids.
| What you want | 3D input |
|---|---|
| Surface z = f(x,y) | f(x,y) = x^2 + y^2 |
| Volume of revolution around x-axis | Surface(f(x)*cos(t), f(x)*sin(t), x, 0, pi, t, 0, 2pi) |
| Sphere centre O, radius r | Sphere(O, r) |
| Plane through 3 points | Plane(A, B, C) |
| Vector from A to B | v = B - A |
| Dot product | u * v |
| Cross product | Cross(u, v) |
Exporting & Sharing for the IA
Menu () → Download as → PNG Image. In the dialog, set scale to 3× or higher for a sharp image that won't pixelate when resized in your document.
Click Share (the icon with an arrow) → copy the link. Add this to your bibliography as: GeoGebra construction - [Your IA Title]. Available at: [link]. Accessed: [date]. This lets the examiner interact with your model.
Paste the PNG into your IA document and add a caption immediately below: Figure 3: GeoGebra plot of logistic growth model f(x) = 500/(1+e^(-0.4(x-8))) fitted to population data. R² = 0.98. Reference this figure number in your prose.
More IA tools
Use the full guide alongside this one to plan, write, and polish your exploration.