Final answer:
To determine the 'a' value of the quadratic function's equation, use the vertex form equation and the given points. The correct value of 'a' is found to be -3 after substituting the points into the equation and solving for 'a'.
Step-by-step explanation:
The student has provided information about a quadratic function which is represented by an upward parabola with a vertex at (-2, 2) and passing through points (-3, 5) and (-1, 5). To find the value of 'a' in the function's equation, we can use the vertex form of a quadratic equation y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. In this case, h = -2 and k = 2, so our equation becomes y = a(x + 2)^2 + 2. We can then plug in the point (-3, 5) to solve for 'a', which will give us:
5 = a(-3 + 2)^2 + 2
5 = a(1)^2 + 2
5 - 2 = a
3 = a
Therefore, the correct answer is C. -3.