The question asks you to evaluate $f(-1)$ for the given quadratic function $f(x) = x^2 + 4x + 8$.

Steps:

1. Substitute $x = -1$ into $f(x) = x^2 + 4x + 8$: $f(-1) = (-1)^2 + 4(-1) + 8$

2. Simplify each term: $f(-1) = 1 - 4 + 8$

3. Combine the terms: $f(-1) = 1 + 8 - 4 = 5$

Final Answer:

The value of $f(-1)$ is 5, so the correct choice is Item 3.

Would you like further explanation or related details? Here are some follow-up questions to expand your understanding:

1. How is the value of $f(-1)$ calculated for a polynomial function?
2. What does the graph of $f(x) = x^2 + 4x + 8$ look like?
3. How do the coefficients of a quadratic function affect its shape?
4. How would you find the vertex of $f(x) = x^2 + 4x + 8$?
5. Can the same substitution process be used for higher-degree polynomials?

Tip: When substituting a value into a function, be careful with signs and order of operations (e.g., exponents before multiplication or addition).