Question

The graphs below have the same shape. What is the equation of the blue

graph?
f(x) = x
g(x) =
?

Answer 1

g(x)=(x-2)^2+1

Explanation:

Answer 2

Option C.
`g(x)=(x+3)^2+1`

Explanation:

The complete question in the attached figure

we know that

The equation of the function f(x) is

`f(x)=x^2`

Is a parabola open upward

The vertex is the point (0,0)

The function g(x) have the same shape

The vertex of the function g(x) is the point (-3,1)

so

The rule of the transformation of f(x) to g(x) is

(0,0) -----> (-3,1)

(x,y) -----> (x-3,y+1)

That means----> The translation is 3 units at left and 1 unit up

therefore

The equation of the function g(x) in vertex form is equal to

`g(x)=(x+3)^2+1`