Answer: First Option
[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]
Step-by-step explanation:
For a quadratic function of the form:
[tex]y = ax ^ 2 + bx + c[/tex]
The vertex form of the equation is:
[tex]y = (x-h) ^ 2 + k[/tex]
Where the vertex is the point (h, k) and [tex]h =-\frac{b}{2a}[/tex]
In this case the equation is: [tex]y=9x^2+9x-1[/tex]
So:
[tex]a=9\\b=9\\c=-1[/tex]
Therefore:
[tex]h =-\frac{9}{2*(9)}[/tex]
[tex]h =-\frac{1}{2}[/tex]
[tex]k=9(-\frac{1}{2})^2+9(-\frac{1}{2})-1\\\\k=-\frac{13}{4}[/tex]
Finally the equation in vertex form is:
[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]
