Can someone lead me through the steps of rewriting the quadratic function in vertex
rewrite the quadratic function in vertex then determine the maximum and minimum and the axis of symmetry:
y = -3x^2 + 18x - 2

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