To determine:One similarity and one difference between the graphs of the equations y2=4xand(y−1)2=4(x−1)

Given: Equations of the graphs:
${\displaystyle y^2=4x\text{and}{(y-1)}^2=4(x-1)}$
The similarity between the two given graphs is as follows:
Both the graphs of the given equations are open from right side and have their directrix parallel to the Y-axis.
The difference between the two given graphs is as follows:
For the equation ${\displaystyle y=4x^2}$, the parabola has its lowest point, that is, the vertex, at the origin (0, 0) opening in the first and third quadrants.
However, for the equation ${\displaystyle {\left(y—1\right)}^2=4{(x-1)}^2}$, the value of h = p = k = 1. So, the coordinates of the vertex of the parabola will be
(h+p,k)=(1+1,1)
=(2,1)
Conclusion: One similarity and one difference between the graphs of the given equations are discussed above.