Parabolas at Work

Roots, vertices and the best fence

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Factored form $a(x - p)(x - q)$ shows the roots $p$ and $q$.
• The vertex is halfway between the roots. In standard form it's at $x = -b/(2a)$.
• Maximum and minimum problems are often about finding a vertex.

Steps

1. The best field
2. Symmetry
3. Roots from factors
4. Find the vertex
5. How low?
6. Standard form
7. Up and down
8. How many roots?