Final answer:
Members of the parabola family f(x) = a(x+3)^2 - 4 share the vertex (-3, -4) and the same axis of symmetry. The 'a' value affects the opening direction and width, and to find a specific parabola passing through a point, we solve for 'a' with the point's coordinates.
Step-by-step explanation:
The family of parabolas described by the function f(x) = a(x+3)^2 - 4 share common characteristics such as the same vertex at (-3, -4) and the axis of symmetry along the line x = -3.
The parameter 'a' affects the opening direction and the width of the parabola. All parabolas in this family will either open upwards (if 'a' is positive) or downwards (if 'a' is negative), but they will not cross the vertex, maintaining the same minimum or maximum point at the vertex.
To find which member passes through a given point, we substitute the point's coordinates into the equation and solve for 'a'. For example, if we want to find the specific member passing through the point (x, y), we would set f(x) = y and solve for 'a'.