Completing the Square Calculator
The Completing the Square Calculator rewrites a quadratic ax² + bx + c in vertex form a(x + d)² + e, which is the key step for integrating or finding the vertex. Enter a, b and c.
Formula
ax² + bx + c = a(x + b/2a)² + (c − b²/4a)
- d = b ÷ (2a) and e = c − b² ÷ (4a).
- The vertex of the parabola is at (−d, e).
x² + 6x + 5
Inputs
- a (x² coefficient): 1
- b (x coefficient): 6
- c (constant): 5
d = 3, e = 5 − 9 = −4, so x² + 6x + 5 = (x + 3)² − 4, vertex (−3, −4).
Frequently asked questions
Why complete the square?
It reveals the vertex, simplifies integration of quadratics, and helps solve equations that do not factor easily.