Convert a quadratic expression ax² + bx + c into vertex form a(x + h)² + k.
Quadratic Coefficients
Input: 1x² + 6x + 5
Vertex Form
f(x) =(x + 3)² - 4
Vertex (h, k)(-3, -4)
About this calculator
Completing the Square
Completing the square is a transformative algebraic technique used to convert a quadratic polynomial ax² + bx + c into the vertex form a(x - h)² + k. This reveals the parabola's vertex (h, k) and symmetry axis.
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Pro Tips
The value inside the parenthesis 'h' corresponds to -b/(2a).
The 'k' value represents the maximum or minimum value of the quadratic function.
If 'a' is positive, the parabola opens upwards (minimum at vertex); if negative, downwards.
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Fun Facts
"The general quadratic formula is essentially derived by applying the 'completing the square' method to ax² + bx + c = 0."
"Geometric algebra by the Babylonians (c. 2000 BC) used similar principles for area calculation problems."
