Write p(x) = 21 + 24x + 6x2 in vertex form.

To do this, complete the square:

p(x) = 21 + 24x + 6x2  =>  p(x) = 6x2 + 24x + 21

Rewrite the first 2 terms as

                                                   6(x^2 + 4x)

then you have p(x) =  6(x2 + 4x                           ) + 21
                            
Now complete the square of x^2 + 4x:

                         p(x) = 6(x^2 + 4x + 4 - 4)            + 21
                                 = 6(x+2)^2 - 24 + 21

                          p(x)  = 6(x+2)^2 - 3        this is in vertex form now.

We can read off the coordinates of the vertex from this:  (-2, -3)