Write the equation of the quadratic function with roots -9 and -3 and a vertex of (-6,-1)

If the roots are -9 and -3 then the function can be written as a binomial product 

a(x+9)(x+3) = a(x^2+12x+27)

The only thing to consider is the coefficient a, which we can use the vertex given as a coordinate.

-1 = a[(-6)^2 + 12(-6) + 27]
-1 = a(36-72+27)
-1 = a(-9)
a = 1/9
so the equation would be 1/9[(x^2+12x+27)]. Depending on the form required to give the answer, you may have to distribute the 1/9 to get

(1/9)x^2 + (4/3)x + 3 = f(x)