We are given the function $f(x) = (x + 3)(x - 3)$, and we are tasked with finding its minimum value.

Step 1: Expand the expression

First, expand the product: $f(x) = (x + 3)(x - 3) = x^2 - 9$ Thus, $f(x) = x^2 - 9$.

Step 2: Identify the type of function

The function $f(x) = x^2 - 9$ is a quadratic function of the form $f(x) = ax^2 + bx + c$, where $a = 1$, $b = 0$, and $c = -9$. Since the coefficient of $x^2$ is positive ($a > 0$), the parabola opens upwards, and it has a minimum value at its vertex.

Step 3: Find the vertex

For a quadratic function $f(x) = ax^2 + bx + c$, the vertex occurs at $x = -\frac{b}{2a}$. In this case, since $b = 0$, the vertex is at: $x = -\frac{0}{2(1)} = 0$

Step 4: Calculate the minimum value

Substitute $x = 0$ into the function $f(x) = x^2 - 9$ to find the minimum value: $f(0) = 0^2 - 9 = -9$

Thus, the minimum value of $f(x)$ is $\boxed{-9}$.

Conclusion:

The correct answer is A) -9.

Would you like more details or have any further questions?

Here are some related questions:

1. What are the general properties of quadratic functions?
2. How do we determine whether a quadratic function opens upwards or downwards?
3. What are the key features of a parabola (vertex, axis of symmetry)?
4. How would the graph of $f(x) = x^2 - 9$ look?
5. How do you find the x-intercepts of a quadratic function?

Tip: Always check if a quadratic function can be factored easily before expanding—it might save time in problem-solving!