Question

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

Answer 1

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
$f(x)=(x-h)^2+k$

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

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

Answer 2

Answer:

g(x)=(x-5)^2+2

Step-by-step explanation: