Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Geometry, trigonometry & Voronoi diagrams

Is a satellite dish really a parabola, and where is its focus?

AA SLAA HL Solid Also in: Modelling, Calculus

Research question

Does the cross-section of a real satellite dish fit a parabola, and does the fitted focus coincide with the position of the receiver arm?

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Why it makes a good exploration

Parabolic reflectors focus signals at a single point. Measuring a real dish, fitting a parabola, and checking whether the receiver is at the focus is a neat test of a geometric property.

The mathematics you'll need

Quadratic functions and the focus–directrix definition (explain)
Least-squares fitting
The reflective property via gradients and angles
Offset dishes as part of a parabola

Modelling the data, step by step

This idea usually needs a quadratic model. See it worked step by step, with a criterion tip at every step: Quadratic: three points, completing the square, regression.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

Where the data comes from

Measure depth at points across a dish (or a wok/bowl) with a straight edge and ruler; measure the receiver position.

GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

A possible outline

Explain the focus–directrix definition.
Measure the profile and fit a parabola.
Find the focus and compare with the receiver.
Demonstrate the reflective property with gradients.
Reflect on offset dishes and measurement error.

Pitfalls that cost marks

Measuring an offset dish as if it were symmetric.
Not converting y = ax² to focal length correctly (f = 1/(4a)).
Too few measurement points.

Showing personal engagement

Measure a dish at home.
Test with a torch and a foil-lined bowl.
Compare with a telescope mirror.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Quadratic functions and the focus–directrix definition (explain); Least-squares fitting
AA HL	Good fit	Quadratic functions and the focus–directrix definition (explain); Least-squares fitting
AI SL	Not a natural fit	The mathematics is mainly AA or HL (calculus or proof beyond AI SL); an AI SL version would need a data-driven, technology-based approach.
AI HL	Not a natural fit	The mathematics is mainly from the AA course; an AI HL version would need modelling with technology, statistics or networks at HL level.

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: measuring an offset dish as if it were symmetric; and not converting y = ax² to focal length correctly (f = 1/(4a)). Say how each one affects your answer.

Use of mathematics (E)

SL: quadratic functions and the focus–directrix definition (explain); least-squares fitting; the reflective property via gradients and angles; offset dishes as part of a parabola, each explained in your own words and carried out correctly.

How geometry & voronoi explorations reach the top bands in general: Geometry, trigonometry & Voronoi diagrams IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Prove the reflective property of the parabola using the gradient and the angle between lines.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL geometry & voronoi exploration adds.

See a complete IA, marked

When is the sea warm enough for our swimming club? A sinusoidal model of sea temperature (AI SL) is a complete geometry & voronoi exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL and AA HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Quadratic functions and the focus–directrix definition (explain), least-squares fitting, the reflective property via gradients and angles and offset dishes as part of a parabola.

Where can I get data for this IA?

Measure depth at points across a dish (or a wok/bowl) with a straight edge and ruler; measure the receiver position. Checked sources and tools: GeoGebra.

Turn this idea into your IA

The planner opens with “Is a satellite dish really a parabola, and where is its focus?” filled in: the question, the maths and the data sources.

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