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: Option D
Explanation
(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)