Question

How do you write `y = (x-2)^2 - 16` in standard form?

Answer 1

`x^2-4x-12`

Explanation:

The standard form of a `color(blue)"quadratic function"` is

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c)color(white)(2/2)|)))`

To obtain `y=(x-2)^2-16" in this form"` expand the brackets and simplify.

`y=(x-2)^2-16=(color(red)(x-2))(x-2)-16`

`=color(red)(x)(x-2)color(red)(-2)(x-2)-16`

`=x^2-2x-2x+4-16`

collecting like terms.

`rArry=x^2-4x-12larr" in standard form"`