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We are given the function:

\[
f(x) = 3x^2 + 9x - 16
\]

We need to find \( f(-8) \). To do this, we substitute \( x = -8 \) into the function.

\[
f(-8) = 3(-8)^2 + 9(-8) - 16
\]

Let me calculate this for you.After substituting \( x = -8 \) into the function \( f(x) = 3x^2 + 9x - 16 \), we get:

\[
f(-8) = 104
\]

Let me know if you'd like further clarification or additional details!

Here are 5 related questions to explore:
1. How would you find \( f(x) \) for other values like \( f(0) \) or \( f(1) \)?
2. Can this function have any real roots? How can we find them?
3. What does the graph of \( f(x) = 3x^2 + 9x - 16 \) look like?
4. How do you find the vertex of a quadratic function like this one?
5. How would the equation change if the constant term was modified?

**Tip:** When solving quadratic functions, it's helpful to remember that substituting values is just one way to explore the behavior of the function. Plotting can give a deeper understanding.

Learn how to solve the quadratic function f(x) = 3x^2 + 9x - 16 by substituting x = -8. This guide explains the steps involved in solving for f(-8), including algebraic substitution and function evaluation, suitable for Grades 9-11.

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