ANSWER
The vertex form is:
[tex]y = {(x + 1)}^{2} - 16[/tex]
EXPLANATION
The given function is:
[tex]y = {x}^{2} + 2x - 15[/tex]
Add and subtract the square of half the coefficient of x.
[tex]y = {x}^{2} + 2x + ( {1)}^{2} - {(1)}^{2} - 15[/tex]
The first three terms for a quadratic trinomial.
[tex]y = {(x + 1)}^{2} - 16[/tex]
This is now in the form
[tex]y = a(x - h) ^{2} + k[/tex]
where (h,k)=(-1,-16) is the vertex
