Answer:
f(x) = 3(x-4)^2 - 33
Explanation:
To convert the function f(x) = 3(x-4)^2 + 3 to standard form, we need to complete the square.
First, we can rewrite the function as follows:
f(x) = 3x^2 - 24x + 36 + 3
Then, we need to add and subtract (24/2)^2 = 36 to complete the square:
f(x) = 3x^2 - 24x + 36 + 3 + 36 - 36
= (3x^2 - 24x + 36) + 3 - 36
= (3(x-4)^2) + 3 - 36
So, the standard form of the function is:
f(x) = 3(x-4)^2 - 33
This is the final form of the function.