Question

What is the vertex form of `y= x^2 + 7x – 6`?

Answer 1

`y=color(green)1(x-color(red)(""(-7/2)))^2+color(blue)(""(-25/4))`
with vertex at
`color(white)("XXX")(color(red)(-7/2),color(blue)(-25/4))`

Explanation:

Given
`color(white)("XXX")y=x^2+7x+6`

Complete the square:
`color(white)("XXX")y=x^2+7xcolor(magenta)(""+(7/2)^2)+6color(magenta)(-(7/2)^2)`

`color(white)("XXX")y=(x+7/2)^2+24/4-49/4`

`color(white)("XXX")y=(x+7/2)^2-25/4`

Some instructors might accept this as a solution,
but in its complete form, the vertex form should look like:
`color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b`
in order to easily read the vertex coordinates.

You should have no difficulty in converting to the form provided in the "Answer".
`color(green)m` must be `color(green)(1)`
converting `(x+7/2)` gives `(x-color(red)(""(-7/2)))`
and `-25/4` is equivalent to `color(blue)(+(-25/4))`