MathematicsGeneralQuality 94 · Exceptional
Why completing the square reveals a parabola’s geometry
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Vicki Thomas Verified Teacher
@author · 2026-08-16 · v1
7 min read
Start with x² + 6x + 5. Half the linear coefficient, 6, to get 3; then add and subtract 3². This gives (x + 3)² - 9 + 5 = (x + 3)² - 4. The algebra does more than solve an equation: it exposes the vertex (-3, -4) and makes every vertical shift visible.
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Why completing the square reveals a parabola’s geometry
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