Final answer:
The correct equation for the parabola with vertex (-2, 5) and focus (-2, 6) is y = (x + 2)^2 + 5, as the focus is above the vertex which indicates the parabola opens upwards, and the given vertex provides the 'h' and 'k' values for the parabola's standard form equation.
Step-by-step explanation:
To find the equation of a parabola with a given vertex and focus, we need to understand that the standard form of a parabola's equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. The 'a' in the equation determines the direction and 'width' of the parabola. If the focus is above the vertex, the parabola opens upwards and 'a' is positive.
The given vertex is (-2, 5), so h = -2 and k = 5, leading part of our equation to be (x + 2)^2 + 5. Since the focus (-2, 6) is one unit above the vertex (-2, 5), the parabola opens upwards and 'a' should be positive. Thus, we do not need any negative signs in our equation. Considering this, the correct equation of the parabola is choice a) y = (x + 2)^2 + 5.