ANSWER
(-3,3)
EXPLANATION
The given function is
[tex]y + 2x + 3 = - (x + 2) ^{2} + 1[/tex]
Expand
[tex]y + 2x + 3 = - x ^{2} - 4x - 4 + 1[/tex]
Rewrite in the form:
[tex]y =a {x}^{2} + bx + c[/tex]
This implies that,
[tex]y = - x ^{2} - 4x - 2 x - 4 + 1 - 3[/tex]
[tex]y = - {x}^{2} - 6x - 6[/tex]
Complete the square to get,
[tex]y = - ( {x}^{2} + 6x) - 6[/tex]
[tex]y = - ( {x}^{2} + 6x + {(3)}^{2} ) - - {(3)}^{2} - 6[/tex]
[tex]y = - {(x + 3)}^{2} +9 - 6[/tex]
[tex]y = - {(x + 3)}^{2} +3[/tex]
The function is now in the form:
[tex]y = a {(x - h)}^{2} +k[/tex]
where (h,k) =(-3,3) is the vertex
