Question

Find the vertex form of y=(x+2)(x-3)

Answer 1

y = (x -
`(1)/(2)` )² -
`(25)/(4)`

Explanation:

Given

y = (x + 2)(x - 3) ← expand factors

= x² - x - 6

Use the method of completing the square

add/ subtract ( half the coefficient of the x- term )² to x² - x

y = x² + 2(-
`(1)/(2)`) x +
`(1)/(4)` -
`(1)/(4)` - 6

= (x -
`(1)/(2)` )² -
`(25)/(4)`