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

(-2, 4)

(-1, 7)

(1, 15)

(2, 9)

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)