What are the coordinates of the vertex for f(x) = 2x2 + 4x + 9?

Your equation  is in the form 
The vertex only relies on "a" and "b" though, so that +9 doesn't really matter in this case.  The vertex of a parabola is located where 

So your x-coordinate is -1.  You need to find f(-1) to find your y-coordinate, and then you list it in the form (-1, y).

Vertex: (-1,7)
Focus: (-1, 57 over 8)
Axis of Symmetry(AOS): x=-1
Directories: y= 55 over 8
X , Y
-3 , 15
-2 , 9
-1 , 7
0 , 9
1 , 5

21/2 or 5/2