Question

write the quadratic function f(x) = 3x^2 -12x +1 in the form f(x) = 3(x-h)^2+k

Answer 1

Complete the square.

Answer 2

\[
3x^2 -12x +1=3(x^2 -4x) +1
\]

Answer 3

You complete the square on \(x^2-4x\).

Answer 4

or cheat, which is what i prefer

Answer 5

\[
x^2+bx = \left(x+\frac b 2\right)^2-\left(\frac b 2\right)^2
\]

Answer 6

cheating method
saves time on test or quiz
vertex of \(ax^2+bx+c\) is always \(-\frac{b}{2a}\)
in your case it is \(-\frac{-12}{2\times 3}=2\)
so you know it will look like
\[3(x-2)^2+k\] and you can find \(k\) by replacing \(x\) by \(2\) in the original expression