Question

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

Answer 1

Translate the graph of x^2 4 spaces to the right and then 2 spaces up.

Answer 2

4

Explanation:

We are given that parent function

`f(x)=x^2`

After translation of parent function

`g(x)=(x-4)^2+2`

We have to find the value of horizontal translation from parent function to the function g(x).

General equation of parabola along y- axis

`y=(x-h)^2+k`

The vertex of function is at (h,k).

The given function is an equation of parabola along y-a xis.

By comparing given function with general equation of parabola then

The vertex of function f(x) is at (0,0).

The vertex of function g(x) is at (4,2).

Therefore, h of f(x) is shift towards right and then we get h of g(x) =4

Hence, the value 4 represents the horizontal transformation from the graph of the parent function f(x) to the graph of the function g(x).