vertex form is [tex]p(x)=a(x-h)^2+k[/tex]basically, just complete the square on the right side
[tex]p(x)=6x^2+24x+21[/tex]group x terms together
[tex]p(x)=(6x^2+24x)+21[/tex]
factor out linear coefient (number in front of the higest power x, in this case x^2)
[tex]p(x)=6(x^2+4x)+21[/tex]
take 1/2 of the linear coefient and square it (4 is linear coefient so take 1/2 of it and square it (4/2=4, 4^2=4)), add positive and negative of it inside the parenthaees (so it equals 0)
[tex]p(x)=6(x^2+4x+4-4)+21[/tex]
factor perfect square trinomial[tex]p(x)=6((x+2)^2-4)+21[/tex]
distribute (don't distribute or expand the squared term)[tex]p(x)=6(x+2)^2-24+21[/tex]
[tex]p(x)=6(x+2)^2-3[/tex]
