Algebra & Equations

Completing the Square

Vertex form a(x−h)²+k of a quadratic.

Formula

h = −b2a, k = c − b²4a

Symbol	Definition	Type & range	Units	Role
a	quadratic coefficient	nonzero real (a ≠ 0)	—	input
b	linear coefficient	real number (ℝ)	—	input
c	constant term	real number (ℝ)	—	input
h	vertex x-coordinate	real number (ℝ)	—	result
k	vertex y-coordinate	real number (ℝ)	—	result

Interactive calculator

Example 1

Givena = 1, b = 6, c = 5

Result
a
1
h
-3
k
-4

Example 2

Givena = 2, b = -8, c = 3

Result
a
2
h
2
k
-5