Analyze the transformation of \( g(x)=(x+3)^{2}-1 \) from \( f(x)=x^{2} \) What type of transformation occurs as a result of +3 inside of parenthesis? Horizontal Shift 3 units Left Vertical Shift 3 units Down Vertical Shift 3 units Up Horizontal Shift 3 units Right

The transformation of \( g(x)=(x+3)^{2}-1 \) from \( f(x)=x^{2} \) involves a horizontal shift due to the \( +3 \) inside the parentheses. Specifically, this indicates that the entire graph of \( f(x) \) is shifted 3 units to the left. So, the new vertex of the parabola moves from the origin to the point (-3, -1). Additionally, the \(-1\) outside of the squared term results in a downward vertical shift of 1 unit. This means the vertex of the graph not only shifts left but also falls one unit down, landing at the coordinates (-3, -1). It's like taking a lovely ride on a rollercoaster – first, you shift your seat left, and then you duck down a little!