Question

which translation maps the graph of the function $f(x)=x^2$ onto the function $g(x)=x^2 - 6x + 6$? left 3 units, down 3 units; left 6 units, down 1 unit; right 6 units, down 1 unit; right 3 units, down 3 units

Explanation:

Step1: Complete the square for $g(x)$

$$\begin{align*} g(x)&=x^2-6x+6\\ &=(x^2-6x+9)-9+6\\ &=(x-3)^2-3 \end{align*}$$

Step2: Compare to $f(x)=x^2$

For a function transformation $f(x-h)+k$: $h=3$ (right 3 units), $k=-3$ (down 3 units)

Answer:

right 3 units, down 3 units