Based on the vertex you provided, which is (-2, -3), the vertex form of a quadratic equation is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola, and \(a\) determines the direction and width of the parabola (if \(a > 0\), it opens upwards; if \(a < 0\), it opens downwards).
Given that the vertex is (-2, -3), we have \(h = -2\) and \(k = -3\). Therefore, the equation can be written as:
\[ y = a(x + 2)^2 - 3 \]
Now, you also need the value of \(a\). Based on the responses you provided, we can identify the following:
- Response 1: \(y = 3(x + 2)^2 - 3\) (opens upwards)
- Response 2: \(y = 3(x - 2)^2 - 3\) (vertex is at (2, -3))
- Response 3: \(y = -3(x + 2)^2 - 3\) (opens downwards, vertex at (-2, -3))
- Response 4: \(y = -3(x - 2)^2 - 3\) (vertex is at (2, -3))
Since you specified that the vertex is (-2, -3), the correct response that represents the vertex form of the equation is:
Response 1: \(y = 3(x + 2)^2 - 3\)
However, if you are indicating a downward-opening parabola, you may have meant Response 3: \(y = -3(x + 2)^2 - 3\).
If the parabola you are analyzing opens upwards, use the first response. If it opens downwards, use the third response. Make sure to choose based on the orientation of the parabola in your graph.