Question

What is the equation of a parabola that is a vertical translation of `-y=x^2-2x+8` of 3 and a horizontal translation of 9?

Answer 1

`- (y' ± 3) = (x' ± 9)^2 -2(x' ±9) + 8`

Explanation:

Vertical translation: `y := y' ± 3`

Horizontal one: `x := x' ± 9`

So, there are four solutions ++/+-/-+/--.

For instance,

`- (y' + 3) = (x' + 9)^2 -2(x' +9) + 8`

`-y - 3 = x^2 + 18x + 81 -2x - 18 + 8`

`-y = x^2 + 16x + 74`