Final answer:
After substituting the x and y values from the given points into the four provided function options, none of them match the required values. Therefore, there is no correct answer among the options, suggesting a typographical error in the question or the answer choices.
Step-by-step explanation:
To determine which function corresponds to the graph that passes through the points (-3, -2.5) and (-4, -3), we should look for a vertex form of a quadratic function, which is generally expressed as y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
None of the given functions has (-3, -2.5) as its vertex, which means we have to check which function passes through both points provided. By substituting the x and y values of each point into the given options, we can find the correct function.
For option (a), substituting x = -3 gives y = (-3 + 4)^2 - 2.5 = 1 - 2.5 = -1.5, which does not match the y-value of the first point. Similarly, for option (b), substituting x = -3, we get y = (-3 - 3)^2 - 4 = 36 - 4 = 32, which also does not match.
Option (c) yields y = (-3 - 4)^2 - 3 = 49 - 3 = 46 for x = -3, and y = (-4 - 4)^2 - 3 = 64 - 3 = 61 for x = -4, neither of which matches the y-values of the given points.
However, for option (d), when we substitute x = -3, we get y = (-3 - (-4))^2 - 3 = 1 - 3 = -2, which is not matching the y-value required. Thus, after substitution, none of the provided options yield the correct y-values for the given points, suggesting a possible typographical error in the question or the answer choices. Hence, the correct function in vertex form that corresponds to these points is not listed among the given options.