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.