Question

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

Answer 1

See full solution process below:

Explanation:

First, expand and square the term in parenthesis:

`y = 3(x - 3)^2 - 12`

`y = 3(color(red)(x) - color(red)(3))(color(blue)(x) - color(blue)(3)) - 12`

`y = 3((color(red)(x) xx color(blue)(x)) - (color(red)(x) xx color(blue)(3)) - (color(red)(3) xx color(blue)(x)) + (color(red)(3) xx color(blue)(3))) - 12`

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

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

We can now fully expand the term in parenthesis by multiplying each individual term within the parenthesis by `color(red)(3)`

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

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

Lastly, we can combine the constants:

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