How do I write the quadratic function

Question

f(x) = 1/2 (6x^2 - 24x + 22) in standard form, and go about graphing the function?

Answer 1

You would complete the square, but let's first clean it up a bit
f(x) = 3x^2 - 12x + 11
now ...
= 3(x^2 - 4x + ..... ) + 11
= 3(x^2 - 4x + 4 - 4) + 11
= 3((x-2)^2 - 4) + 11
= 3(x-2)^2 - 12 + 11
= 3(x-2)^2 - 1

up to you ....