Question

How do you write in vertex form for `y=x^2 + .6x - 11` by completing the square?

Answer 1

The general squared binomial is `(x+a)^2 = x^2+2ax+a^2`

Given the equation `y= x^2+.6x-11`

If the coefficient of `x` is `(0.6)`
then
in terms of the general form `a=0.3` and `a^2 = 0.09`

Writing as a completed square:
`color(white)("XXXXX")` `y = (x+0.3)^2 -11 -0.09`

`color(white)("XXXXX")` `y = (x - (-0.3))^2 + (-11.09)`

which is the vertex form
`color(white)("XXXXX")`with the vertex at `(-0.3,-11.09)`