To evaluate $f(1)$, we simply substitute 1 into the given function expression:

$f(1) = 3 \cdot 1^2 + 3 \cdot 1 - 6$

Step-by-step calculation:

1. $1^2 = 1$
2. $3 \cdot 1 = 3$
3. $3 \cdot 1 = 3$
4. Now sum the terms: $f(1) = 3 + 3 - 6 = 0$

Final answer:

$f(1) = 0$

Would you like further details or clarification?

Here are five related questions to expand on this topic:

1. How would you evaluate $f(2)$ if the function were given by $f(x) = 3x^2 + 3x - 6$?
2. What is the general process for evaluating a quadratic function at a specific point?
3. How do you determine the zeros of the function $f(x) = 3x^2 + 3x - 6$?
4. What is the vertex of the quadratic function $f(x) = 3x^2 + 3x - 6$?
5. How does changing the constant term affect the graph of a quadratic function?

Tip:

Always simplify step-by-step when substituting values into polynomial expressions to avoid mistakes.