Since the function increases when x goes from -∞ to 5, and decreases when x goes from 5 to ∞, then the parabola has a maximum at its vertex, therefore it is a concave down parabola.
The general form of a concave down parabola, with vertex (5,9) is:
[tex]\begin{gathered} y-9=-k(x-5)^2, \\ \text{where k is a positive constant.} \end{gathered}[/tex]Answer: Option d)
[tex]f(x)=-(x-5)^2+9.[/tex]
