Let's evaluate the function $f(x) = 3x^2 - 5x + 1$ at $x = -2$.

Given: $f(x) = 3x^2 - 5x + 1$

Substitute $x = -2$:

$f(-2) = 3(-2)^2 - 5(-2) + 1$

Now, calculate each term step by step:

1. $(-2)^2 = 4$

2. $3 \times 4 = 12$

3. $-5 \times (-2) = 10$

4. Add these results together: $12 + 10 + 1 = 23$

So, the value of $f(-2)$ is $23$.

If you have further questions or need more details, please let me know!

Here are some related questions to explore:

1. What is $f(1)$ for the function $f(x) = 3x^2 - 5x + 1$?
2. What is the maximum or minimum value of this quadratic function?
3. How do you determine the direction of the parabola represented by this function?
4. What are the solutions (roots) of $f(x) = 0$?
5. How would you find the derivative of this function?
6. Can you find the integral of this quadratic function?
7. What are the x-intercepts of the function?
8. How would you rewrite the function in vertex form?

Tip: When substituting values into an expression, carefully follow the order of operations: parentheses, exponents, multiplication and division, addition and subtraction (PEMDAS).