Question

Write in vertex form y= -3x^2-18x-31

Answer 1

I'm not sure if your asking for an entire equation but the points for the vertex would be (-3,-4)

Answer 2

`y = - 3( {x + 3)}^(2) - 4`

Step-by-step explanation

The given function is

`y = - 3 {x}^(2) - 18x - 31`

Factor -3

`y = - 3( {x}^(2) + 6x) - 31`

Add and subtract the square of half the coefficient of x.

`y = - 3( {x}^(2) + 6x + {3}^(2) ) - - 3( {3)}^(2) - 31`

`y = - 3( {x}^(2) + 6x + {3}^(2) ) + 27 - 31`

Apply perfect squares,

`y = - 3( {x +3)}^(2) - 4`

The vertex form is:

`y = - 3( {x +3)}^(2) - 4`