The vertex is (-1,8)
The y intercept = (0,7)
This means that c = 7
The x coordinate of the vertex = -b / [ 2a] = -1
This implies that b = 2a
So we have that [ using (-1,8) ]
8 = a(-1)^2 + 2a(-1) + 7
8 = a - 2a + 7
8 = -a + 7
1 = -a
-1 =a
And b = 2(-1) = -2
So....the form is
y = -x^2 - 2x + 7
So
a + b + 2c =
-1 -2 + 2(7) =
-3 + 14
11