Completing the Square

Vertex form of a quadratic: y = a(x - h)^2 + k The vertex is (h, k) — the highest or lowest point of the parabola. Completing the square converts standard form (ax^2 + bx + c) into vertex form. This lets you: - Find the vertex directly - Solve equations that don't factor nicely - Understand the geometry of the parabola

To complete the square for x^2 + bx: 1. Take half of b: frac{b}{2} 2. Square it: left(frac{b}{2}right)^2 3. Add and subtract this value [formula]

Example: Rewrite x^2 + 6x + 5 in vertex form.