Okay, here we have this:
Considering the provided information, we are going to find the requested equation of the parabola, so we obtain the following:
According to the information given by substituting in the form of the parabola we have the following equation:
[tex](x-2)^2=8(y-2)[/tex]
Let's solve for y:
[tex]\begin{gathered} y-2=\frac{(x-2)^2}{8} \\ y-2=\frac{x^2-4x+4}{8} \\ y=\frac{1}{8}x^2-\frac{1}{2}x+\frac{1}{2}+2 \\ y=\frac{1}{8}x^2-\frac{1}{2}x+\frac{5}{2} \end{gathered}[/tex]
Finally we obtain that the correct answer is the option D.
