By completing the square

MATHEMATICS · Subjective · AoPS · Mathematics · Quadratic Equations - Part 2 · Quadratic Equations - Part 2

Problem

By completing the square, show that the vertex of the parabola y=ax2+bx+cy = ax^2 + bx + c, where a≠0, has coordinates (−b2a,c−b24a).a \neq 0, \text{ has coordinates } \left( \frac{-b}{2a}, c - \frac{b^2}{4a} \right).

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