Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 2x 1?

Answer 1

Shift 1 unit to the left to perform the translation maps the vertex of f(x) onto the vertex of the function g(x).

It is given that the function  $\rm f(x) = x^2$ and function  $\rm g(x)= x^2+2x+1$

It is required to find the translation maps of the vertex of the graph of f(x) onto the vetrex of the graph of g(x).

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have two functions first one:

$\rm f(x) = x^2$   and

$\rm g(x)= x^2+2x+1$

For the function f(x) the vertex is (0, 0) as shown in the graph.

We can write g(x) as a:

$\rm g(x)= x^2+2x+1\\\\\rm g(x) = (x+1)^2$∵ $\rm (a+b)^2 = a^2+2ab+b^2$

And the vertex of the graph of g(x) is (-1, 0)   [Shown in the graph]

For f(x) vertex point is (0, 0)  and

For g(x) vetex point is (-1 , 0)

It is clear that the if shift vertex point f(x) to -1 unit we get (-1, 0) ie.

(x, y) ⇒⇒ (x-1, y)

(0, 0) ⇒⇒ (0-1, 0) ⇒⇒ (-1, 0)

Thus, shift 1 unit to the left to perform the translation maps the vertex of f(x) onto the vertex of the function g(x).

Learn more about the function here:

brainly.com/question/5245372