The given graph represents a downward parabola with centre (h,k) = (2,-4) and it passes through (8,-7) .
Here we use the following formula
[tex] y=a(x-h)^2+k [/tex]
[tex] -7=a(8-2)^2-4 [/tex]
[tex] -3 = 36a=> a =-\frac{1}{12} [/tex]
So the required equation is
[tex] y=-\frac{1}{12}(x-2)^2-4 [/tex]
or
[tex] y =-\frac{x^2}{12}+\frac{x}{3}-\frac{13}{3} [/tex]
