Question

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

(−2, 4)
(−1, 7)
(1, 15)
(2, 9)

Answer 1

To answer this quickly the answer is (-1,7)

Answer 2

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

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)