vetex form is:
y = a(x-h)^2+ky=a(x−h)2+k and the vertex is (h, k)(h,k)
to get vertex form we must complete the square:
y=3x^2+6x-24y=3x2+6x−24
isolate the x terms:
y +24 =3x^2+6xy+24=3x2+6x
factor out 3 so the coefficient of x^2x2 is 1 which is required to complete the square:
y +24 =3(x^2+2x)y+24=3(x2+2x)
now complete the square
ax^2 +bx +cax2+bx+c, a = 1, c= (1/2b)^2c=(12b)2
c=(1/2(2))^2 = 1^2 = 1c=(12(2))2=12=1
y +24 +3c=3(x^2+2x +c)y+24+3c=3(x2+2x+c) notice 3c3c 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 cc
y +24 +3(1)=3(x^2+2x +1)y+24+3(1)=3(x2+2x+1)
finish the square:
y +27=3(x +1)^2y+27=3(x+1)2
y =3(x +1)^2 -27y=3(x+1)2−27
so our vertex is (-1, -27)(−1,−27)
remember the form is y = a(x-h)^2+ky=a(x−h)2+k so the sign of the h term changes.
