Question

what value represents the horizontal translation from the graph of the parent function f(x)=x^2 to the graph of the function g(x)=(x+5)^2+3

Answer 1

The graph $y=x^2$ is the parent function with a vertex at the origin (0, 0).  In our parabola, we have (x+5)^2 which indicates side to side movement of the vertex.  The standard form for the parabola is $(x-h)^2+k=y$, where h and k are the coordinates of the vertex.  If your parabola has (x+5)^2, it originally was written as (x-(-5)).  So our vertex has moved 5 units to the left.  It also moves up 3 but you are only asking about the horizontal movement.  5 units to the left.