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?

Dec 15, 2015

- (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,

$- \left(y ' + 3\right) = {\left(x ' + 9\right)}^{2} - 2 \left(x ' + 9\right) + 8$

$- y - 3 = {x}^{2} + 18 x + 81 - 2 x - 18 + 8$

$- y = {x}^{2} + 16 x + 74$