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

(−2, 4)
(−1, 7)
(1, 15)
(2, 9)

The answer to your question is  V ( -1 , 7)

Step-by-step explanation:

Data

                   f(x) = 2x² + 4x + 9

1.- Use "y" instead of f(x)

                      y = 2x² + 4x + 9

2.- Subtract 9 in both sides and simplify

                     y - 9 = 2x² + 4x + 9 - 9

                     y - 9 = 2x² + 4x

3.- Factor 2 in the right side

                     y - 9 = 2(x² + 2x         )

4.- Complete the perfect square trinomial

                    y - 9 + 2 = 2(x² + 2x + 1)

5.- Simplify

                         y - 7 = 2(x + 1)²

6.- Get the Vertex

                           V ( -1 , 7)