Instructions: Given the function, state the vertex.y=−3(x+7)2−6𝑦=−3(𝑥+7)2−6Vertex =(=( ,, )

1. Break Down the Problem

We need to find the vertex of the quadratic function given in vertex form: $y = -3(x + 7)^2 - 6$

2. Relevant Concepts

In the vertex form of a quadratic function, which is of the form: $y = a(x - h)^2 + k$ the vertex of the parabola is given by the point $(h, k)$, where $h$ and $k$ correspond to the horizontal and vertical shifts from the origin, respectively.

3. Analysis and Detail

From the equation:

• The term $(x + 7)$ can be reinterpreted as $(x - (-7))$, indicating a shift to the left by 7 units from the origin.
• The $k$ value is $-6$, indicating a downward shift by 6 units.

Thus, we can identify:

• $h = -7$
• $k = -6$

4. Verify and Summarize

So, the coordinates of the vertex are: $\text{Vertex} = (-7, -6)$

Final Answer

Vertex = $(-7, -6)$