Question

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?

Answer 1

\(y = x^2\)

\(x = \pm \ \sqrt{ y}\)

\(\bar x = x + 3\)

\(\bar x = \pm \ \sqrt{ y} + 3\)

\(\pm \ \sqrt{ y} = \bar x - 3 \)

\(y = ( \bar x - 3)^2 \)

Answer 2

in general speak

\(y = f(x)\)
\(x = f^{-1}(y)\)
\(\bar x = x + a\)
\(\bar x = f^{-1}(y) + a\)
\(f^{-1}(y) = \bar x - a\)
\(y = f(\bar x - a)\)