1. Rewrite the quadratic funtion from standard form to vertex form. \[ f(x)=x^{2}-12 x+46 \] $f(x)=(x-6)^{2}+10$ $f(x)=(x-12)^{2}+46$ $f(x)=(x-6)^{2}+46$ $f(x)=(x-12)^{2}+10$

Step 1 ：Given the quadratic function in standard form: \(f(x)=x^{2}-12 x+46\)

Step 2 ：Rewrite the quadratic function from standard form to vertex form. The vertex form of a quadratic function is given by \(f(x) = a(x-h)^2 + k\), where \((h, k)\) is the vertex of the parabola.

Step 3 ：To convert the standard form \(f(x) = ax^2 + bx + c\) to the vertex form, we can complete the square. In this case, we have \(a = 1\), \(b = -12\), and \(c = 46\).

Step 4 ：Calculate the values of \(h\) and \(k\) using the formulas \(h = -b/2a\) and \(k = c - b^2/4a\).

Step 5 ：Substitute \(a = 1\), \(b = -12\), and \(c = 46\) into the formulas to get \(h = 6.0\) and \(k = 10.0\).

Step 6 ：Substitute \(h\) and \(k\) into the vertex form to get the final answer.

Step 7 ：\(\boxed{f(x) = (x - 6)^2 + 10}\) is the vertex form of the function.