Functions and Graphs
Rewriting a quadratic function to find the vertex of its graph

Write the quadratic function in the form $f(x)=a(x-h)^{2}+k$.
Then, give the vertex of its graph.
\[
f(x)=3 x^{2}-18 x+26
\]

Writing in the form specified: $f(x)=\square$

Vertex: (‥)

Step 1 ：Given the function \(f(x)=3x^{2}-18x+26\).

Step 2 ：Factor out a 3 from the first two terms: \(f(x)=3(x^{2}-6x)+26\).

Step 3 ：To complete the square, take half of the coefficient of x, square it, and add and subtract it inside the parenthesis. Half of -6 is -3, and \((-3)^2\) is 9.

Step 4 ：So, \(f(x)=3[(x^{2}-6x+9)-9]+26\).

Step 5 ：This simplifies to \(f(x)=3[(x-3)^{2}-9]+26\).

Step 6 ：Finally, distribute the 3 and simplify to get the function in the form \(f(x)=a(x-h)^{2}+k\): \(f(x)=3(x-3)^{2}-27+26\).

Step 7 ：So, \(f(x)=3(x-3)^{2}-1\).

Step 8 ：The vertex of a function in the form \(f(x)=a(x-h)^{2}+k\) is at the point (h, k).

Step 9 ：\(\boxed{\text{So, the vertex of the function } f(x)=3(x-3)^{2}-1 \text{ is at the point } (3, -1)}\).