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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The function that translates the graph of the parent function \( f(x)=x^{2} \) vertically up 6 units is \( g(x)=x^{2}+6 \). By adding 6, each point on the parabola shifts up by 6 units, creating a new vertex at the point (0, 6). Conversely, the function \( g(x)=x^{2}-6 \) would translate the graph down 6 units, resulting in a vertex at (0, -6). This illustrates how adding or subtracting values affects the vertical positioning of a graph.
