Completing the Square

Find the vertex, every time

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $x^2 + bx$ becomes a perfect square by adding $(b/2)^2$.
• Vertex form $(x - h)^2 + k$ shows the vertex $(h, k)$.
• Completing the square solves every quadratic, even ones that don’t factor nicely.

Steps

1. A perfect square
2. Why it’s called that
3. Completing it, literally
4. Vertex
5. Find the vertex
6. Highest point
7. Solve by completing the square