Question

What is the vertex form of `y= x(x - 7)`?

Answer 1

`y=1(x-7/2)^2+(-49/4)`

Explanation:

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

Given
`color(white)("XXX")y=x(x-7)`

`color(white)("XXX")y=x^2-7x`

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

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

`color(white)("XXX")y=color(green)(1)(x-color(red)(7/2))^2+(color(blue)(-49/4))`