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Completing the Square Calculator

Enter a, b, and c of ax² + bx + c to convert to vertex form a(x − h)² + k — with the vertex, axis of symmetry, and real roots, plus full step-by-step working.

Vertex form:  a(x − h)² + k,  where h = −b / (2a) and k = c − b² / (4a)
a x2 + b x + c

Coefficient a must not be 0 (otherwise it is not a quadratic). Decimals and negatives are fine.

Results

Vertex form
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Vertex (h, k)
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Axis of symmetry
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h = −b / (2a)
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k = c − b² / (4a)
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Real roots
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Step-by-step (completing the square)