Final answer:
The function f(x) = 3x² + 6x + 6 is already in standard form.
Step-by-step explanation:
To write the function f(x) = 3x² + 6x + 6 in standard form, we need to arrange the terms in descending order of degree. The standard form of a quadratic function is ax² + bx + c = 0, where the coefficients a, b, and c can be any real numbers.
Start with the given function:
f(x) = 3x² + 6x + 6
Ensure the terms are ordered by descending powers of x:
3x² + 6x + 6
No need to change the order as it's already in the correct form.
Identify the coefficients a, b, and c:
a=3, b=6, c=6
Write the standard form :ax² + bx + c
f(x) = 3x² + 6x + 6
So, the step-by-step process confirms that the given quadratic function is already in standard form, and the correct representation is option a)