What is the vertex of the function f(x) = x² + 12x?
(-6, -36), (-6, 0), (6, 0), (6, -36)

Solution:

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

= -36

Therefore, the vertex is (-6, -36).

What is the vertex of the function f(x) = x² + 12x?
(-6, -36), (-6, 0), (6, 0), (6, -36)

Summary:

The vertex of the function f(x) = x² + 12x is (-6, -36).