If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).
\(y = x^{2} - 6x + 11\)
\( y = a(x - h)^{2} + k\)
\(a(x - h)^{2} + k = a(x^{2} - 2hx + h^{2}) + k\)
\(ax^{2} - 2ahx + ah^{2} + k = x^{2} - 6x + 11\)
Comparing, we have
\(a = 1\)
\(2ah = 6 \implies 2h = 6; h = 3\)
\(ah^{2} + k = 11 \implies (1 \times 3^{2}) + k = 11\)
\(9 + k = 11 \implies k = 2\)
\(\therefore a + h + k = 1 + 3 + 2 = 6\)
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