Given the function:

\[
f(x) = 4x^2 - 3x + 7
\]

We want to find \( f(-2) \).

1. Substitute \( x = -2 \) into the function:

\[
f(-2) = 4(-2)^2 - 3(-2) + 7
\]

2. Calculate each term:

\[
(-2)^2 = 4 \quad \text{so} \quad 4(-2)^2 = 4 \times 4 = 16
\]
\[
-3(-2) = 6
\]

Now, combine all terms:

\[
f(-2) = 16 + 6 + 7 = 29
\]

Thus, \( f(-2) = 29 \).

Would you like more details on any of the steps?

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Here are 5 related questions:
1. What is \( f(0) \) for the same function?
2. How would you find the roots of \( f(x) = 0 \)?
3. What is the derivative of \( f(x) = 4x^2 - 3x + 7 \)?
4. How would you calculate \( f(1) \)?
5. Can you express \( f(x) \) in vertex form?

**Tip**: Always simplify powers and multiplication before dealing with signs when substituting values into functions.

Discover how to evaluate the quadratic function f(x) = 4x^2 - 3x + 7 at f(-2) using substitution. Learn key algebraic concepts and step-by-step calculations. Ideal for students in Grades 8-10.

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