Question

What is the vertex form of `y=x(x-3)`?

Answer 1

`y = (x - 3/2)^2 - 9/4`

Explanation:

`y = x(x - 3)` `rArr y = x^2 -3x`

Use the process of completing the square.

`y = x^2 -3x + (3/2)^2 - (3/2)^2`

Note in the previous line `+ (3/2)^2 - (3/2)^2 =0`, so the value of the expression has not changed.

`y = (x - 3/2)^2 - 9/4`