If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).

A.

-4

B.

-3

C.

0

D.

6

Correct answer is D

\(y = x^{2} - 6x + 11\)

\( y = a(x - h)^{2} + k\)

\(a(x - h)^{2} + k = a(x^{2} - 2hx + h^{2}) + k\)

\(ax^{2} - 2ahx + ah^{2} + k = x^{2} - 6x + 11\)

Comparing, we have

\(a = 1\)

\(2ah = 6 \implies 2h = 6; h = 3\)

\(ah^{2} + k = 11 \implies (1 \times 3^{2}) + k = 11\)

\(9 + k = 11 \implies k = 2\)

\(\therefore a + h + k = 1 + 3 + 2 = 6\)