A parabola can be written in the vertex form as follows:
[tex]y=a(x-h)^2+k[/tex]
Where:
[tex](h,k)[/tex]
Are the coordinates of the vertex.
Since the vertex is at:
[tex]\begin{gathered} (h,k)=(-2,1) \\ \end{gathered}[/tex]
The equation is:
[tex]\begin{gathered} y=a(x-(-2))^2+1 \\ y=a(x+2)+1 \end{gathered}[/tex]
But, since it is a horizontal parabola:
[tex]\begin{gathered} x=a(y-k)+h \\ so\colon \\ x=a(y-1)^2-2 \end{gathered}[/tex]
Therefore, the only valid option is:
[tex]x=4(y-1)^2-2[/tex]
