What is the vertex of the function f(x) = x² + 12x?

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Finding the Vertex of the Function

To find the vertex of the quadratic function f(x) = x² + 12x, we can use the vertex formula or complete the square. The vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

where (h, k) is the vertex. We can also use the formula for the x-coordinate of the vertex:

h = -b / (2a)

In our function, we have:

  • a = 1 (the coefficient of x²)
  • b = 12 (the coefficient of x)
  • c = 0 (the constant term)

Now, substituting the values of a and b into the vertex formula:

h = -12 / (2 * 1) = -12 / 2 = -6

So, the x-coordinate of the vertex is -6.

Next, to find the y-coordinate (k), we substitute x = -6 back into the original function:

f(-6) = (-6)² + 12(-6)
        = 36 - 72
        = -36

Thus, the y-coordinate of the vertex is -36.

Final Result

In conclusion, the vertex of the function f(x) = x² + 12x is:

(-6, -36)

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