Write p (x) = 21 + 24x + 6x2 in vertex form. p (x) = (x + ) 2 -

P (x) = 6 (x+2) ^2-3

...

Group x terms

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

factor out the quadratic coefient

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

take 1/2 of linear coefient and square it

4/2=2, 2^2=4

add negative and positive inside parenthasees

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

factor perfect square

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

expand

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

p (x) = 6 (x+2) ^2-3