Question

What is the vertex form of `4y = x(x+12)+13`?

Answer 1

`y=1/4(x-(-6))^2+(-6)`
`color(white)("XXXXXXXXXXX")`with vertex at `(-6,-6)`

Explanation:

The general vertex form is
`color(white)("XXX")y=m(x-a)^2+b`
with vertex at `(a,b)`

Given:
`color(white)("XXX")4y=x(x+12)+13`
Expand the right side
`color(white)("XXX")4y=x^2+12x+13`
Complete the square
`color(white)("XXX")4y=x^2+12xcolor(green)(+6^2)+13color(green)(-36)`
Rewrite as a squared binomial (and combine the constant)
`color(white)("XXX")4y=(x+6)^2-24`
Divide both sides by `4`
`color(white)("XXX")y=1/4(x-(-6))^2+(-6)`