Question

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

Answer 1

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

$g(x)=(x+4)^{2} -3$

Answer 2

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