ANSWER
[tex]y= -3{(x + 4)}^{2} + 2[/tex]
EXPLANATION
The given function is:
[tex]y= -3x^2-24x-46[/tex]
Factor -3 for the first 2 terms.
[tex]y= -3(x^2 + 8x)-46[/tex]
We add and subtract the square of the coefficient of x.
[tex]y= -3(x^2 + 8x + {(4)}^{2} ) - - 3( {4)}^{2} -46[/tex]
Factor the perfect square trinomial.
[tex]y= -3 {(x + 4)}^{2} ) + 48 -46[/tex]
The vertex form is:
[tex]y= -3{(x + 4)}^{2} + 2[/tex]
