Finding the Vertex of the Parabola: y = (x+3)² - 6

To solve this problem, we'll utilize the properties of the vertex form.

• Step 1: Identify the form of the quadratic equation. It is given as $y = (x+3)^2 - 6$.
• Step 2: Recognize this as a vertex form equation $y = a(x-h)^2 + k$.
• Step 3: Compare to identify $h$ and $k$. Here, $h = -3$ and $k = -6$.
• Step 4: Determine the vertex of the parabola, which is $(-3, -6)$.

In the vertex form, $a(x-h)^2 + k$, the vertex is simply $(h, k)$. For the equation $y = (x+3)^2 - 6$, $h$ is $-3$ and $k$ is $-6$.
Thus, the vertex of the parabola is $(-3, -6)$.

Therefore, the solution to the problem is $(-3, -6)$.