Question

The graphs below have the same shape. what is the equation of the blue graph? Please help!!!!!

Answer 1

G(x) shifts 4 units to the left and 3 down
equation
G(x) = (x + 4)^2 - 3

answer is C.
G(x) = (x + 4)^2 - 3

Answer 2

we have

`f(x)=x^(2)`

The vertex of f(x) is the point
`(0,0)`

The vertex of g(x) is the point
`(-4,-3)` ----> see the graph

So

The rule of the translation is

`f(x)------> g(x)`

`(x,y)-----> (x-4,y-3)`

that means

the translation is
`4` units to the left and
`3` units down

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

`g(x)=(x-h)^(2) +k`

where

(h,k) is the vertex

`(h,k)=(-4,-3)`

Substitute

`g(x)=(x+4)^(2) -3`

therefore

the answer is the option C

`g(x)=(x+4)^(2) -3`