Complete the square: vertex and max or min

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Learn it To write y = ax² + bx + c in vertex form y = a(x − h)² + k: factor a out of the first two terms, add and subtract (half the x-coefficient)², and simplify. The vertex is (h, k): a minimum if a > 0, a maximum if a < 0.

Example: Write y = 2x² − 12x + 7 in vertex form.

y = 2(x² − 6x) + 7.
y = 2(x² − 6x + 9 − 9) + 7 = 2(x − 3)² − 18 + 7.
y = 2(x − 3)² − 11: minimum value −11 at x = 3.

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