The vertex form of a parabolic function has the general formula:
f(x) = a(x-h)^2 + k where (h,k) represent the vertex of the parabola.
Therefore, to write the given equation in vertex form, we will need to transform it to the above formula as follows:
y = 9x^2 + 9x – 1
y = 9(x^2 + x) – 1
y = 9(x^2 + x + 1/4 – 1/4)-1
y = 9((x+1/2)^2 – 1/4)-1
y = 9(x + 1/2)^2 – 9/4 – 1
y = 9(x + 1/2)^2 – 13/4 ————-> The equation in vertex form
If you need the vertex of the parabola, it will simply be (-1/2, -13/4)