1. Rewrite $y=3 x^{2}-12 x-5$ in the form of $y=a(x-h)^{2}+k$ by completing the square.

Step 1 ：Factor out 3 from the terms \(3x^2 - 12x\) to get \(3(x^2 - 4x)\)

Step 2 ：To complete the square, we can square \(x - 2\) to get \(x^2 - 4x + 4\), so \(3(x^2 - 4x) = 3[(x - 2)^2 - 4] = 3(x - 2)^2 - 12\)

Step 3 ：Now, we have \(y = 3(x - 2)^2 - 12 - 5 = 3(x - 2)^2 - 17\)

Step 4 ：So, the equation is in the form \(y = a(x - h)^2 + k\) with \(a = 3\), \(h = 2\), and \(k = -17\)

Step 5 ：\(\boxed{y = 3(x - 2)^2 - 17}\)