Write - 3x^2-18-31 in vertex form.

Get into form a (x-h) ²+k

complete the square

-3x²-18x-31

group x terms

(-3x²-18x) - 31

undistribute the - 3

-3 (x²+6x) - 31

take 1/2 of the linear coefient (6) and squaer it

6/2=3, 3²=9

add positive and negative of it inside parenthasees

-3 (x²+6x+9-9) - 31

complete the square

-3 ((x+3) ²-9) - 31

expand

-3 (x+3) ²+27-31

-3 (x+3) ²-4 is vertex form