Question

What is the vertex form of `y= (9x-6)(3x+2)+4x^2+5x`?

Answer 1

`y=31(x+5/62)^2-1513/124`

Explanation:

`y=(9x-6)(3x+2)+4x^2+5x`

= `27x^2+18x-18x-12+4x^2+5x`

= `31x^2+5x-12`

= `31(x^2+5/31x)-12`

= `31(x^2+2xx5/62xx x+(5/62)^2-(5/62)^2)-12`

= `31(x+5/62)^2-31(5/62)^2-12`

= `31(x+5/62)^2-25/124-12`

or `y=31(x+5/62)^2-12 25/124`

i.e. `y=31(x+5/62)^2-1513/124`

and vertex is `(-5/62,-12 25/124)`

graph{y=31(x+5/62)^2-1513/124 [-3, 3, -20, 20]}