Answer:
Option D.
Step-by-step explanation:
The vertex form of a parabola along y-axis is
[tex]y=a(x-h)^2+k[/tex] ...(1)
where, (h,k) is vertex and a is a constant.
From the given graph it is clear that the vertex of the parabola is (0,2). So, h=0 and k=2.
[tex]y=a(x-0)^2+2[/tex]
[tex]y=ax^2+2[/tex] ...(2)
The graph passing through (6,5). Substitute x=6 and y=5 in the above equation.
[tex]5=a(6)^2+2[/tex]
[tex]5-2=36a[/tex]
[tex]3=36a[/tex]
[tex]\frac{3}{36}=a[/tex]
[tex]\frac{1}{12}=a[/tex]
Substitute [tex]a=\frac{1}{12}[/tex] in equation (2).
[tex]y=\frac{1}{12}x^2+2[/tex]
Therefore, the correct option is D.
