Vertex form equation
y = a(x - h)² + k
We need to solve it by completing quadratic form
To complete the quadratic form, multiply the equation by 4. We multiply it by 4 so the coefficient of x² is in complete quadratic form and the coefficient of x is an even number.
y = 9x² + 9x - 1
--------------------- (multiply 4)
4y = 36x² + 36x - 4
Change the quadratic expression into complete quadratic form
Add +9 to the both side
4y = 36x² + 36x - 4
4y + 9 = 36x² + 36x + 9 - 4
4y + 9 = (6x + 3)² - 4
4y = (6x + 3)² - 4 - 9
4y = (6x + 3)² - 13
------------------------------ divide by 4
[tex]y = \frac{1}{4} (6x+3)^{2}- \frac{13}{4} [/tex]
