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

nagasenaz 2021-02-05 Answered
To determine:One similarity and one difference between the graphs of the equations
\(\displaystyle{y}^{{2}}={4}{x}{\quad\text{and}\quad}{\left({y}-{1}\right)}^{{2}}={4}{\left({x}-{1}\right)}\)

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Expert Answer

odgovoreh
Answered 2021-02-06 Author has 14992 answers
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.
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