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The given function is \( f(x) = x^2 + 3 \). Let's calculate the required values:

### a) \( f(6) \)
Substitute \( x = 6 \) into the function:

\[
f(6) = 6^2 + 3 = 36 + 3 = 39
\]

### b) \( f(-6) \)
Substitute \( x = -6 \) into the function:

\[
f(-6) = (-6)^2 + 3 = 36 + 3 = 39
\]

Thus:
- \( f(6) = 39 \)
- \( f(-6) = 39 \)

Would you like a detailed explanation on how the calculations were performed, or do you have any questions?

Here are some related questions you might find useful:
1. What is the general behavior of a quadratic function like \( f(x) = x^2 + 3 \)?
2. How would you find the x-intercepts of the function \( f(x) = x^2 + 3 \)?
3. What is the vertex of the function \( f(x) = x^2 + 3 \)?
4. How would the graph of \( f(x) = x^2 + 3 \) compare to \( f(x) = x^2 \)?
5. Can the function \( f(x) = x^2 + 3 \) ever produce a negative value?

**Tip:** When evaluating functions, always check the order of operations, especially when squaring negative numbers to avoid sign errors.

Given that f(x) = x^2 + 3, work out the value of f(6) and f(-6).

Learn how to evaluate the quadratic function f(x) = x^2 + 3 at specific points like f(6) and f(-6). This problem covers key concepts in basic algebra and function evaluation. Suitable for students in Grades 7-9.

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