Final answer:
The first step to find the vertex is to rewrite the quadratic function f(x) = x² + 6x + 9 in vertex form by completing the square. The equation is already a perfect square, making the vertex of the parabola (-3, 0).
Step-by-step explanation:
The first step in calculating the vertex of the quadratic function f(x) = x² + 6x + 9 is to express the quadratic in vertex form, which is f(x) = a(x - h)² + k. To complete the square and transform the given quadratic equation into vertex form, we should first factor out the coefficient of the x² term, which is 1 in this case. Since the coefficient is already 1, we can proceed to the next step which involves finding the perfect square.
The given quadratic is already a perfect square because (x + 3)² = x² + 6x + 9. Therefore, the function in vertex form is f(x) = (x + 3)², which makes the vertex of the parabola (-3, 0).