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

To determine:One similarity and one difference between the graphs of the equations
$$\displaystyle{y}^{{2}}={4}{x}{\quad\text{and}\quad}{\left({y}-{1}\right)}^{{2}}={4}{\left({x}-{1}\right)}$$

• Questions are typically answered in as fast as 30 minutes

Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

odgovoreh
Given: Equations of the graphs:
$$\displaystyle{y}^{{2}}={4}{x}{\quad\text{and}\quad}{\left({y}-{1}\right)}^{{2}}={4}{\left({x}-{1}\right)}$$
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 $$\displaystyle{y}={4}{x}^{{2}}$$, 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 $$\displaystyle{\left({y}—{1}\right)}^{{2}}={4}{\left({x}-{1}\right)}^{{2}}$$, 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.