write a possible equation for the graph.

Explanation:

Step1: Identify vertex form of quadratic

The graph is a parabola. The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola.

Step2: Determine the vertex

From the graph, the vertex of the parabola is $(- 4,-2)$. So, $h=-4$ and $k = - 2$. Then the equation becomes $y=a(x + 4)^2-2$.

Step3: Find the value of a

We can use another point on the graph, say $(-3, - 1)$. Substitute $x=-3$ and $y = - 1$ into $y=a(x + 4)^2-2$. [ \begin{align*} -1&=a(-3 + 4)^2-2\ -1&=a(1)^2-2\ -1&=a-2\ a&=1 \end{align*} ]

Answer:

$y=(x + 4)^2-2$