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Completing the Square Calculator

Rewrite any quadratic expression ax² + bx + c in vertex form a(x + h)² + k by completing the square.

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Coefficient a

Coefficient b

Coefficient c

Formula

Completing the square rewrites ax² + bx + c as a(x + h)² + k. This is useful for finding the vertex of a parabola: vertex = (−h, k).

ax² + bx + c = a(x + h)² + k

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter coefficients a, b, and c.
2Click Calculate to rewrite in vertex form.
3The result shows the expression as a(x+h)²+k.

Examples

Rewrite x² + 6x + 5 in vertex form

1.Enter a=1, b=6, c=5.
2.h = 6/(2×1) = 3.
3.k = 5 − 1×3² = 5 − 9 = −4.
4.Result: (x+3)² − 4.

Result: 1(x + 3.0000)² − 4.0000

Rewrite 2x² − 8x + 7 in vertex form

1.Enter a=2, b=-8, c=7.
2.h = -8/(2×2) = -2.
3.k = 7 − 2×(−2)² = 7 − 8 = −1.
4.Result: 2(x − 2.0000)² − 1.0000.

Result: 2(x − 2.0000)² − 1.0000

Frequently Asked Questions

It is a method of rewriting a quadratic ax²+bx+c as a(x+h)²+k by adding and subtracting a perfect square term.

The vertex form a(x+h)²+k directly shows the vertex of a parabola at point (−h, k).

It helps find the maximum or minimum of a quadratic, graph parabolas, and solve quadratic equations.

A negative a means the parabola opens downward. The calculator handles negative a values correctly.

Expand a(x+h)²+k: a(x²+2hx+h²)+k = ax² + 2ahx + (ah²+k).

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CalculateMe Team

Last updated: 2026-07-13

Completing the Square Calculator - Rewrite Quadratics in Vertex Form | CalculateMe | CalculateMe