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)
