What are the coordinates of the vertex for f(x) = 3x² + 6x + 3?

Solution:

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.

Given, the equation is y = 3x² + 6x + 3

Here, a = 3, b = 6 and c = 3

So, h = -6/2(3)

h = -6/6

h = -1

4ac = 4(3)(3)

4ac = 36

So, k = [36 - (6)²]/4(3)

k = (36 - 36)/12

k = 0

Therefore, the coordinates of the vertex is (h, k) = (-1, 0).

What are the coordinates of the vertex for f(x) = 3x² + 6x + 3?

Summary:

The coordinates of the vertex for f(x) = 3x² + 6x + 3 are (-1, 0).