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\(y = x{}^{2} + 6x + 7\)

\(y - 7 = x{}^{2} + 6x\)

\(y - 7 - 9 = x{}^{2} + 6x + 9\)

\(y - 16 = (x + 3){}^{2}\)

\(y = (x + 3){}^{2} + 16\)