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

Solution:

Given, the equation is y = 2x² + 4x + 9

We have to find the coordinates of the vertex.

For any equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Here, a = 2, b = 4 and c = 9

So, h = -4/2(2)

h = -4/4

h = -1

4ac = 4(2)(9)

4ac = 72

So, k = [72 - (4)²]/4(2)

k = (72 - 16)/8

k = 56/8

k = 7

Therefore, the coordinates of the vertex is (h, k) = (-1, 7).

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

Summary:

The coordinates of the vertex for f(x) = 2x² + 4x + 9 are (-1, 7).