## anonymous one year ago Translations: if the home equation is f(x) = x^2, why does f(x) = (x-3)^2 move the equation to the right instead of the left?

1. IrishBoy123

$$y = x^2$$ $$x = \pm \ \sqrt{ y}$$ $$\bar x = x + 3$$ $$\bar x = \pm \ \sqrt{ y} + 3$$ $$\pm \ \sqrt{ y} = \bar x - 3$$ $$y = ( \bar x - 3)^2$$

2. IrishBoy123

in general speak $$y = f(x)$$ $$x = f^{-1}(y)$$ $$\bar x = x + a$$ $$\bar x = f^{-1}(y) + a$$ $$f^{-1}(y) = \bar x - a$$ $$y = f(\bar x - a)$$

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