Given equation :y = 9x^2 + 9x – 1.
We need to convert it in vertex form y= a(x-h)^2 +k
In order to find the vertex form, we need to find the values of a, h and k.
a is the coefficient of x^2.
Therefore, a = 9.
Now, we need to find the value of h.
h = -b/2a = -9/2(9) = -1/2.
Plugging x=-1/2 in given equation, we get
y = 9(-1/2)^2 +9(-1/2) -1.
y = 9/4 -9/2 -1
y = 9/4 -18/4 - 4/4
y = -13/4
We got h=-1/2 and k= -13/4.
Therefore, vertex form is
[tex]y = 9(x+\frac{1}{2}) ^2 -\frac{13}{4}[/tex].
