[tex]\begin{gathered} x=\frac{1}{8}(y-5)^2-1,\text{ vertex :(-1, 5)} \\ \\ \text{axis of symmetry: y=5} \end{gathered}[/tex]
EXPLANATION
First, let's find the vertex.
From the graph, the vertex is (-1, 5).
It is symmetric about y = 5
Length of the Latus rectom (a) =2 x 4 = 8
Therefore, the equation of the graph is;
[tex]y=\frac{1}{a}(y-5)^2-1[/tex]
Substitute a = 8
[tex]x=\frac{1}{8}(y-5)^2-1[/tex]
