To find $f(-1)$ given the function $f(x) = -3x^2 + 10x + 13$, you need to substitute $x = -1$ into the function.

Step-by-Step Solution:

1. Start with the function: $f(x) = -3x^2 + 10x + 13$

2. Substitute $x = -1$ into the function: $f(-1) = -3(-1)^2 + 10(-1) + 13$

3. Calculate each term:

   • $(-1)^2 = 1$
   • $-3 \times 1 = -3$
   • $10 \times (-1) = -10$
   • $13$ remains as is.

4. Combine these values: $f(-1) = -3 - 10 + 13$

5. Simplify: $f(-1) = -13 + 13 = 0$

So, $f(-1) = 0$.

Would you like a detailed explanation or have any questions? Here are some related questions you might consider:

1. How would the result change if $x = 2$?
2. What is the vertex of the parabola represented by $f(x)$?
3. How can you determine the x-intercepts of $f(x)$?
4. What is the axis of symmetry for the function $f(x)$?
5. How does the sign of the coefficient of $x^2$ affect the shape of the graph?

Tip: Always double-check your substitutions and arithmetic when working with functions to avoid simple mistakes.