Question

Write the quadratic function f(x) = 3x^2 - 6x + 9 in vertex form.

Answer 1

factor a 3 out of the first two terms
\[f(x)=3(x^2-2x)+9\]
then "complete the square"
\[f(x)=3(x-1)^2+k\] as for \(k\) replace \(x\) by 1 in the original expression to see what you get

Answer 2

that is, compute
\[f(1)=k=3-6+9=6\]