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

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To find the vertex of the quadratic function f(x) = 3x² + 6x + 3, we can use the formula for the vertex of a parabola given in the standard form f(x) = ax² + bx + c. The coordinates of the vertex (h, k) can be found using the formulas:

  • h = -b / (2a)
  • k = f(h)

In this function, we have:

  • a = 3
  • b = 6
  • c = 3

First, let’s calculate h:

h = -b / (2a)
  = -6 / (2 * 3)
  = -6 / 6
  = -1

Now that we have h = -1, we can find k by substituting h back into the function:

k = f(-1)
  = 3(-1)² + 6(-1) + 3
  = 3(1) - 6 + 3
  = 3 - 6 + 3
  = 0

Therefore, the vertex of the quadratic function is at the point:

(h, k) = (-1, 0)

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

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