To identify the vertex on the graph, we need to know whether you are referring to the vertex of a quadratic function or a different type of graph. However, generally speaking, the vertex for a standard quadratic function of the form \( y = a(x - h)^2 + k \) is given by the point \((h, k)\).
From your responses, I can infer that the options given are potential vertices. If you have a specific quadratic equation or the context of the graph, please share that for a more precise identification.
Based on the points you've given, the one with the lowest y-value would typically be the vertex for a downward-opening parabola. Hence:
- \( (−12,0) \)
- \( (−10,0) \)
- \( (−11,−1) \)
- \( x=−11 \)
From these, if we're looking for a typical vertex, \( (−11,−1) \) appears to be a vertex at the lowest point, assuming the function opens upwards.
Please confirm if there is more context or specific data so we can refine this response!