g) Describe the transformation of the graphof \( f(x)=-(x-7)^{2}+6 \) from the graph of \( y=x^{2} \)

This equation represents a parabola that opens downward, and it originates from the standard parabola \( y = x^2 \). The transformation begins with shifting the graph 7 units to the right due to the \((x-7)\) term, placing the vertex at \( (7, 6) \). Next, the \(-1\) in front of the squared term indicates a reflection over the x-axis, causing the parabola to open downward instead of upward. Finally, the added \( +6 \) shifts the entire graph up by 6 units, completing the transformation. To visualize this better, picture taking the basic U-shaped graph of \( y = x^2 \), moving it over to the right to create a new bump starting at \( (7, 0) \), flipping it upside down, and then sliding it up so its peak sits at \( (7, 6) \). Voilà! You now have the elegant downturn of \( f(x) = - (x - 7)^2 + 6 \).