To complete the square for the function f(x) = (3/2)x^2 - 12x + 6, we can follow these steps:
Factor out the coefficient of x^2 from the first two terms:
f(x) = (3/2)(x^2 - 8x) + 6
Take half of the coefficient of x (-8), square it, and add and subtract it inside the parentheses:
f(x) = (3/2)(x^2 - 8x + 16 - 16) + 6
Rearrange the terms inside the parentheses and simplify:
f(x) = (3/2)((x - 4)^2 - 16) + 6
Distribute the coefficient of (x - 4)^2 and simplify:
f(x) = (3/2)(x - 4)^2 - 12 + 6
Combine the constants and simplify:
f(x) = (3/2)(x - 4)^2 - 6
Therefore, the completed square form of the function f(x) = (3/2)x^2 - 12x + 6 is f(x) = (3/2)(x - 4)^2 - 6.