Question

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

Answer 1

ANSWER

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

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:

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

Answer 2

Answer:

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