Question

What is the vertex form of `y= (x+2)(x - 7)`?

Answer 1

minimum vertex `-81/4` at `(5/2, -81/4)`

Explanation:

`y = (x + 2)(x - 7) = x^2 - 5 x - 14`

use completing a square to solve
`y = x^2 - 5 x - 14`

`y = (x -5/2)^2 -(-5/2)^2 - 14`

`y = (x -5/2)^2 - 25/4 - 56/4`

`y = (x -5/2)^2 -81/4`

since `(x -5/2)^2` is +ve value, therefore it has a minimum vertex `-81/4` at `(5/2, -81/4)`