Can someone lead me through the steps of rewriting the quadratic function in vertex form?

Rewrite the quadratic function in vertex form ... 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