To find \( f(-2) \), we first need to express the function in its standard form. Given:

\[
18f(x) = -x^2 + 18
\]

We want to isolate \( f(x) \) by dividing both sides of the equation by 18:

\[
f(x) = \frac{-x^2 + 18}{18}
\]

Now, substitute \( x = -2 \) into the function:

\[
f(-2) = \frac{-(-2)^2 + 18}{18}
\]

Simplifying:

\[
f(-2) = \frac{-4 + 18}{18} = \frac{14}{18} = \frac{7}{9}
\]

Thus, \( f(-2) = \frac{7}{9} \).

Would you like further details or have any questions?

Here are some related questions you might explore:
1. What is the general form of a quadratic function?
2. How does the sign of the leading coefficient affect the graph of a quadratic function?
3. Can you find the vertex of the function \( f(x) = \frac{-x^2 + 18}{18} \)?
4. How do you determine the domain and range of this quadratic function?
5. What is the effect of dividing the quadratic function by a constant?

**Tip:** Always simplify the expression inside parentheses first when substituting values into a function.

Discover how to find f(-2) for the quadratic function 18f(x) = -x^2 + 18. This problem involves simplifying expressions and substitution, making it perfect for students in Grades 9-10.

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