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

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To find the coordinates of the vertex for the quadratic function given by the equation f(x) = 2x² + 4x + 9, we can use the vertex formula. The vertex (h,k) of a quadratic function of the standard form f(x) = ax² + bx + c can be found using the following formulas:

  • h = -b / (2a)
  • k = f(h)

In this case, the values for a, b, and c are:

  • a = 2
  • b = 4
  • c = 9

We can start by calculating h:

h = -b / (2a) = -4 / (2 * 2) = -4 / 4 = -1

Now that we have h, we need to find k. We do this by substituting h back into the function f(x):

k = f(h) = f(-1) = 2(-1)² + 4(-1) + 9 = 2(1) - 4 + 9 = 2 - 4 + 9 = 7

Thus, the coordinates of the vertex are (-1, 7).

In conclusion, the vertex of the function f(x) = 2x² + 4x + 9 is located at the coordinates (-1, 7).

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