162x + 731 = - y - 9x-2 vertex form

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