The graphs below have the same shape. what is the equation of the red graph?

Option D.

Step-by-step explanation:

we have

-----> the parent function

The vertex of the function F(x) is the origin (0,0)

The vertex of the function G(x) is the point (0,-1)

so

The rule of the translation is equal to

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

That means ------> The translation is 1 unit down

Applying the rule of the translation to F(x)

F(x)-------> G(x)

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: