Express (3x^{2} – 6x + 10) in the form (a(x – b)^{2} + c), where a, b and c are integers. Hence state the minimum value of (3x^{2} – 6x + 10) and the value of x for which it occurs.
Explanation
(3x^{2} – 6x + 10)
(3(x^{2} – 2x) + 10)
(3[x^{2} – 2x + (frac{1}{2}(-2))^{2}] + 10 – 3)
= (3(x – 1)^{2} + 7)
The minimum value is 7 and this occurs at x – 1 = 0 ==> x = 1.