Complete the square to write the equation "y=3x^2+6x-24" in graphing form?

1 Answer
May 20, 2018

#y =3(x +1)^2 -27#

vertex is #(-1, -27)#

Explanation:

vetex form is:

#y = a(x-h)^2+k# and the vertex is #(h, k)#

to get vertex form we must complete the square:

#y=3x^2+6x-24#

isolate the x terms:

#y +24 =3x^2+6x#

factor out 3 so the coefficient of #x^2# is 1 which is required to complete the square:

#y +24 =3(x^2+2x)#

now complete the square

#ax^2 +bx +c#, a = 1, #c= (1/2b)^2#

#c=(1/2(2))^2 = 1^2 = 1#

#y +24 +3c=3(x^2+2x +c)# notice #3c# added to the left side, that is because we have to add the same value to both sides and the right side has 3 factored out.

replace the #c#

#y +24 +3(1)=3(x^2+2x +1)#

finish the square:

#y +27=3(x +1)^2#

#y =3(x +1)^2 -27#

so our vertex is #(-1, -27)#

remember the form is #y = a(x-h)^2+k# so the sign of the h term changes.