Looking at y = 2x^2 + 4x + 9, we see it is in the form y = ax^2 + bx + c where
a = 2
b = 4
c = 9
Plug these into h = -b/(2a) to get
h = -b/(2a)
h = -4/(2*2)
h = -1
Then plug this into the function to get
f(x) = 2x^2 + 4x + 9
f(-1) = 2(-1)^2 + 4(-1) + 9
f(-1) = 2(1) + 4(-1) + 9
f(-1) = 2-4+9
f(-1) = -2+9
f(-1) = 7
So the vertex is at (-1,7)
