Final answer:
The vertex of the quadratic function f(x) = x^2 + 12x is (-6, -36), found by using the formula -b/(2a) and substituting the x-coordinate back into the function.
Step-by-step explanation:
The vertex of a quadratic function, such as f(x) = x^2 + 12x, can be found using the formula -b / (2a), where a and b are the coefficients of x^2 and x, respectively.
The standard form of a quadratic is ax^2 + bx + c.
For the given function, a = 1 and b = 12, so the x-coordinate of the vertex, also known as the axis of symmetry, is
-b / (2a) = -12 / (2*1) = -6.
To find the y-coordinate of the vertex, we substitute the x-coordinate back into the function:
f(-6) = (-6)^2 + 12*(-6)
= 36 - 72
= -36.
Therefore, the vertex of the function is (-6, -36).