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.