Question

How do you write `y= 3(x-3)^2-12` in standard form?

Answer 1

`y=3x^2-18x+15`

Explanation:

The equation of a `color(blue)"parabola in standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c ;a≠0)color(white)(2/2)|)))`

First step is to distribute `(x-3)^2=(x-3)(x-3)`

Each term in the second bracket is multiplied by each term in the first bracket. This can be achieved as follows.

`(color(red)(x-3))(x-3)`

`=color(red)(x)(x-3)color(red)(-3)(x-3)`

distribute the brackets.

`=x^2-3x-3x+9=x^2-6x+9`

If you know the FOIL method then you can use it.

The function is now.

`y=3(x^2-6x+9)-12`

distributing by 3 gives.

`y=3x^2-18x+27-12`

`rArry=3x^2-18x+15larrcolor(red)" in standard form"`