Question

The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x). (−1, −8) (−3, −4) (−1, −6) (−5, −6)

Answer 1

Answer: (-1,-6)

Step-by-step explanation:

x^2+6x+3

g(x) = f(x-2)

replace all value of x in the f(x) function to (x-2)

(x-2)^2 + 6(x-2) + 34

(x-2)(x-2) + 6(x-2) + 34

expand through FOIL and distribution

x^2-4x+4+6x-12+3

combine like terms

x^2+2x-5

-b/2a = x value of vertex

-2/2(1) = x value

x value = -1

plug in -1 for all values of x in the g(x) equation to solve for y value

(-1)^2+2(-1)-5

1-2-5 = -6

y = -6

x = -1

(x,y) = (-1,-6)