Question

How do you write `y= (x-2) ^2+ 6` in standard form?

Answer 1

See a solution process below:

Explanation:

We can use this rule to expand the term in parenthesis:

`(color(red)(x) - color(blue)(y))^2 = color(red)(x)^2 - 2color(red)(x)color(blue)(y) + color(blue)(y)^2`

`y = (color(red)(x) - color(blue)(2))^2 + 6`

`y = color(red)(x)^2 - (2 * color(red)(x) * color(blue)(2)) + color(blue)(2)^2 + 6`

`y = x^2 - 4x + 4 + 6`

`y = x^2 - 4x + 10`