What value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x – 4)2 + 2?

The value of horizontal shift is that means graph of parent function is shifted to right by 4 units.

Step-by-step explanation:  

We have been given a parent function and another function . We are asked to determine the horizontal translation from the graph of the parent function to the graph of the function g(x).

Let us recall translation rules.  

Horizontal translation:  

Vertical translation:

Upon looking at our both functions, we can see that parent function is shifted to right by 4 units and upwards by 2 units to get the the function g(x).

Therefore, the value of horizontal translation is , which indicates the graph is shifted to right by 4 units.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

1. perpendicular

2. parallel

3. perpendicular