Rewrite ax²+bx+c into vertex form a(x−h)²+k and identify the vertex coordinates.
Completing the square transforms ax²+bx+c into vertex form a(x−h)²+k, where (h,k) is the vertex of the parabola. The vertex x-coordinate is h = −b/(2a) and the y-coordinate is k = c − b²/(4a).
Vertex coordinates
h = -b/(2a), k = c - b²/(4a)
Vertex form
a(x - h)² + k
It reveals the vertex of a parabola, makes it easy to find the axis of symmetry, and is the basis for deriving the quadratic formula.
The quadratic formula is derived by completing the square on the general form ax²+bx+c=0 and solving for x.