Final answer:
The parent function family of f(x) = (x-1)^2+3 is the quadratic function family.
Step-by-step explanation:
The parent function family of f(x) = (x-1)^2+3 is the quadratic function family. A quadratic function is a second-order polynomial where the highest power of the variable is 2. In this case, the function f(x) = (x-1)^2+3 represents a quadratic function with a vertex at (1, 3) and opens upwards.
Quadratic functions are represented by the general form y = ax^2 + bx + c, where a, b, and c are constants. In the given function, a = 1, b = -2, and c = 4.
For example, the original function f(x) = (x-1)^2+3 is a specific quadratic function in the quadratic function family, with the transformation of shifting the vertex right 1 unit and up 3 units from the parent function y = x^2.