Vertex Form Converter

Standard Form ax² + bx + c

x² coeff.

x coeff.

constant

2x² − 4x − 6

Examples

Vertex Form a(x − h)² + k

stretch / flip

h-shift

v-shift

2(x − 1)² − 8

Examples

Result

Enter coefficients and press Convert to see both forms, the vertex, and the graph.

Standard Form

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Vertex Form

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Vertex (h, k)

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Axis of Symmetry

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y-Intercept

Opens Up

Understanding Vertex Form a(x − h)² + k

f(x) = a(x − h)² + k

Each parameter controls a specific transformation of the basic parabola y = x²:

h — horizontal shift. The graph moves right by h units (or left if h is negative). Note the minus sign inside: (x − h).

k — vertical shift. The graph moves up by k units (or down if k is negative).

a — stretch and direction. |a| > 1 narrows the parabola; 0 < |a| < 1 widens it. Negative a flips it upside down.

Completing the square is the algebraic process that converts standard form to vertex form — it literally "completes" a perfect-square trinomial.

Why Vertex Form is Useful

vertex = (h, k) · axis: x = h · max/min at y = k

Vertex form makes it trivial to read off the most important features of a parabola at a glance: