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

We can start by figuring out the axis of symmetry.

y = x² + 12x = x (x + 12)

So roots are x = -12 or 0

Therefore axis of symmetry is x   =   (-12 + 0) / 2   =   -6

We got x-coordinate of vertex. Now plug in x=-6 to solve for y.

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

Therefore vertex is (-6, -36).

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