1. Which of the following functions translates the graph of the parent function $$ f(x)=x^{2} $$ vertically up 6 units? $$ g(x)=x^{2}+6 $$ $$ g(x)=x^{2}-6 $$

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To determine which function translates the graph of the parent function $$ f(x) = x^2 $$ vertically up 6 units, we need to understand how vertical translations work in function transformations.

1. **Vertical Translation**: 
   - If we add a positive constant $$ k $$ to a function $$ f(x) $$, the graph of the function shifts vertically upwards by $$ k $$ units.
   - Conversely, if we subtract a constant $$ k $$, the graph shifts downwards.

2. **Given Functions**:
   - $$ g(x) = x^2 + 6 $$
   - $$ g(x) = x^2 - 6 $$

3. **Analysis**:
   - For $$ g(x) = x^2 + 6 $$:
     - This function adds 6 to the output of $$ f(x) $$. Therefore, it translates the graph of $$ f(x) $$ upwards by 6 units.
   - For $$ g(x) = x^2 - 6 $$:
     - This function subtracts 6 from the output of $$ f(x) $$. Therefore, it translates the graph of $$ f(x) $$ downwards by 6 units.

4. **Conclusion**:
   - The function that translates the graph of the parent function $$ f(x) = x^2 $$ vertically up 6 units is $$ g(x) = x^2 + 6 $$.

Thus, the correct answer is $$ g(x) = x^2 + 6 $$.
$$ g(x) = x^2 + 6 $$ translates the graph of $$ f(x) = x^2 $$ vertically up 6 units.

1. Which of the following functions translates the graph of the parent function \( f(x)=x^{2} \) vertically up 6 units? \( g(x)=x^{2}+6 \) \( g(x)=x^{2}-6 \)

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