Use transformations of $$ f(x)=x^{2} $$ to graph the following function. $$ h(x)=(x-6)^{2}-3 $$ What transformations are needed to graph the function $$ h(x)=(x-6)^{2}-3 $$ ? Choose the correct answer below. A. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the right by 6 units and vertically shifted down by 3 units. B. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the right by 6 units and vertically shifted up by 3 units. C. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the left by 6 units and vertically shifted down by 3 units. D. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the left by 6 units and vertically shifted up by 3 units.

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1. The parent function is $$ f(x)=x^2 $$.
2. The function $$ h(x) = (x-6)^2 - 3 $$ shows two clear transformations compared to $$ f(x) $$:
   - The term $$(x-6)$$ inside the square indicates a horizontal shift.
   - The $$-3$$ outside the square indicates a vertical shift.
3. A function of the form $$ (x-h)^2 $$ represents a horizontal shift to the right by $$ h $$ units when $$ h $$ is positive. Here, $$ h=6 $$, so the graph is shifted to the right by 6 units.
4. A function of the form $$ f(x)-k $$ represents a vertical shift downward by $$ k $$ units when $$ k $$ is positive. Here, $$ k=3 $$, so the graph is shifted downward by 3 units.
5. Therefore, the correct transformations are: the graph of $$ f(x)=x^2 $$ should be horizontally shifted to the right by 6 units and vertically shifted down by 3 units.

The correct answer is A.
The graph of $$ f(x)=x^{2} $$ should be shifted 6 units to the right and 3 units down to obtain $$ h(x)=(x-6)^{2}-3 $$.

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