Question

identify the graph of $f(x)=-x^{2}-6x - 6$.

Explanation:

Step1: Identify the form of the function

The function $f(x)=-x^{2}-6x - 6$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-1$, $b = - 6$, $c=-6$.

Step2: Determine the direction of the parabola

Since $a=-1<0$, the parabola opens down - ward.

Step3: Find the x - coordinate of the vertex

The formula for the x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. Substituting $a=-1$ and $b = - 6$ into the formula, we get $x=-\frac{-6}{2\times(-1)}=-3$.

Step4: Find the y - coordinate of the vertex

Substitute $x = - 3$ into the function $f(x)=-x^{2}-6x - 6$. Then $f(-3)=-(-3)^{2}-6\times(-3)-6=-9 + 18-6=3$. So the vertex is $(-3,3)$.

Answer:

The graph is a downward - opening parabola with vertex at $(-3,3)$. Without seeing the specific labels on the provided graphs, you would look for a downward - opening parabola centered around $x=-3$ with a peak at $y = 3$.