f(x) = x2 + 12x [Given]
Standard equation of a curve in vertex form is
f (x) = ax2 + bx + c
Vertex is represented as (h,k) where
X-coordinate of the vertex is h = -b/2a
and k = f(h)
Comparing the given equation with the standard form
a = 1, b = 12 and c = 0
So we get
h = -12/2(1) = - 6
Substituting the value of h in f (x)
k = f(h)= f (-6) = (-6)2 + 12 (-6)
= 36 - 72
Therefore, the vertex is (-6, -36).
The vertex of the function f(x) = x2 + 12x is (-6, -36).