Which phrase best describes the translation from the graph y=6x^2 to the graph of y=6 (x+1)^2?

Solution: The Equation of pre image is

               →   y = 6 x²

And the equation of image after translation is

→ y = 6 (x+1)²

The point (x,y) of preimage is translated to (x+1,y+0) i.e x is translated horizontally right by 1 units and y coordinate is not translated i.e neither vertically up or down remains unchanged.

As both of them represents parabola, one having vertex at (0,0) and another having vertex at (-1,0).But the curve is shifted 1 unit backwards along X axis because the origin has been shifted from (0,0) to (-1,0).