complete the square
to get y=a(x-h)²+k
(h,k) is vertex
x=h is axis of symmetry
if a>0 then the verex is a minimum
if a<0 then the vertex is a maximum
so
groupu x terms
y=(-3x²+18x)-3
undistribute -3
y=-3(x²-6x)-3
take 1/2 of the liear coefient then square it
-6/2=-3, (-3)²=9
add positve and negative of that inside parentheasees
y=-3(x²-6x+9-9)-3
factor perfect squrae
y=-3((x-3)²-9)-3
expand/distribute
y=-3(x-3)²+27-3
y=-3(x-3)²+24
vertex is (3,24)
-3<0 so it is a maximum
axis of symmetry is x=3
