Question

The function f(x) = x^2 − 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

(5, −6)
(5, −8)
(1, −6)
(3, −8)

Answer 1

Answer:

(5, -6)

Step-by-step explanation:

x² - 6x + 3 = (x - 3)² - 6

Vertex: (3, -6)

Vertex of g(x): (5, -6)

Answer 2

Answer:

The vertex is (5, -6)

Step-by-step explanation:

Given $f(x)=x^2-6x+3\\\therefore g(x)=f(x-2)=(x-2)^2-6(x-2)+3=x^2-10x+19$

we now write $g(x)$ in a completed square/vertex form

therefore,

$g(x)=x^2-10x+(-5)^2+19-(-5)^2\\\implies g(x)=(x-5)^2+19-25=(x-5)^2-6$

the vertex is (5, -6)