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

The vertex of the quadratic function f(x) = x² + 12x can be found by using the formula for the vertex, which is given by the coordinates (h, k) in the standard form of the quadratic equation, y = a(x – h)² + k.

First, we need to convert the equation into the standard form. To do so, we can complete the square:

f(x) = x² + 12x
     = (x² + 12x + 36) - 36
     = (x + 6)² - 36

Now, it’s clear that the function is in the form y = a(x – h)² + k, where:

• h = -6
• k = -36

Thus, the vertex of the function is at the point (-6, -36).

In summary, the vertex of the function f(x) = x² + 12x is (-6, -36), which represents the maximum or minimum point of the parabola described by this quadratic function.