Question

identify the graph of (f(x)=-2x^{2}-8x - 12).

Explanation:

Step1: Identify the form of the function

The function $f(x)=-2x^{2}-8x - 12$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-2$, $b = - 8$, $c=-12$.

Step2: Determine the direction of the parabola

Since $a=-2<0$, the parabola opens downwards.

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 $x=-\frac{b}{2a}$. Substitute $a=-2$ and $b = - 8$ into the formula: $x=-\frac{-8}{2\times(-2)}=-\frac{-8}{-4}=-2$.

Step4: Find the y - coordinate of the vertex

Substitute $x = - 2$ into the function $f(x)=-2x^{2}-8x - 12$. $f(-2)=-2\times(-2)^{2}-8\times(-2)-12=-2\times4 + 16-12=-8 + 16-12=-4$. So the vertex is $(-2,-4)$.

Answer:

The graph is a parabola that opens downwards with vertex at $(-2,-4)$. Without seeing the specific options clearly (due to the blurry image), you would look for a graph that has these characteristics.