There is a typo in the quadratic term.
I am goint to solve this question assuming that the correct expression is 162x + 731 = - y - 9x^2
Now, you should know that the vertex form is y = a(x - h)^2 + k, where the vertex is (h,k).
So, we just must transform the quadratic function into that form. To do that you must complete squares. I will do it step by step
start: 162 x + 731 = - y - 9x^2
1) Transpose terms:
y = - 9x^2 - 162x + 731
2) extract common factor ot the two terms with x^2 and x.
y = - 9 (x^2 + 18x) + 731
3) complete squares for x^2 + 18x, which is (x + 9)^2 - 81
=> y = - 9 [ ( x + 9)^2 - 81 ] + 731
4) solve the square brackets
=> y = - 9 (x + 9)^2 - 9*81 + 731
=> y = - 9(x + 9)^2 -729 + 731
=> y = - 9 (x + 9)^2 + 2
Answer: y = - 9 (x + 9)^2 + 2
