nagasenaz

2021-02-05

To determine:One similarity and one difference between the graphs of the equations
${y}^{2}=4x\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}{\left(y-1\right)}^{2}=4\left(x-1\right)$

odgovoreh

Expert

Given: Equations of the graphs:
${y}^{2}=4x\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}{\left(y-1\right)}^{2}=4\left(x-1\right)$
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 $y=4{x}^{2}$, 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 ${\left(y—1\right)}^{2}=4{\left(x-1\right)}^{2}$, 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.

Do you have a similar question?