contestada

What is the equation of the translated function, g(x), if f(x) = x2? g(x) = (x + 5)2 + 2 g(x) = (x + 2)2 + 5 g(x) = (x – 2)2 + 5 g(x) = (x – 5)2 + 2

Respuesta :

nobillionaireNobley
Given the graph of the function f(x) which is described by a parabola with the vertex at (0, 0) and the graph of the translated function g(x) which is described by a parabola with the vertex at (5, 2).

Notice, that the vertex of the translated function is 5 units to the right and 2 units up of the graph of f(x).

Thus, g(x) is obtained by translating the function f(x) 5 units to the right and 2 units up.

Recall that given a function described by a parabola with vertex at (h, k) as
[tex]f(x)=(x-h)^2+k[/tex]

A translation of a units to the right and b units up will result in
[tex]f'(x)=(x-h-a)^2+k+b[/tex]

Therefore, the equation of the translated function, g(x) is given by
[tex]g(x)=(x-5)^2+2[/tex]

Translation of graph means to move the graph on the horizontal and vertical axis by shifting it. The equation of the translated function is,

[tex]g(x)=(x-5)^2+2[/tex]

Given information-

The given equation is,

[tex]f(x)=x^2[/tex]

In the given graph the function [tex]f(x)[/tex] is at the origin with the coordinate (0,0).

As the power of variable is 2. Thus the function is the quadratic function and the graph is made for the parabola.

What is translation graph?

Translation of graph means to move the graph on the horizontal and vertical axis by shifting it.

Original graph is shifted at (5,2). Thus the translated function [tex]g(x)[/tex] has the coordinate (5,2).

The standard form of the parabola can be given as,

[tex]f(x)=(x-h)^2+k[/tex]

Here h,k are the vertex of the parabola.

The transaction is 5 units right and the 2 units up. Thus the equation can be given as,

[tex]g(x)=(x-5)^2+2[/tex]

Hence, the equation of the translated function is,

[tex]g(x)=(x-5)^2+2[/tex]

Learn more about the translation function here;

https://brainly.com/question/26238840

Otras preguntas