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

To graph the function \( h(x)=(x-6)^{2}+2 \), we begin with the parent function \( f(x)=x^{2} \). The expression inside the parentheses, \( (x-6) \), indicates a horizontal shift. Since it is \( (x-6) \), we shift the graph to the right by 6 units. The \( +2 \) outside the square indicates a vertical shift, moving the graph upwards by 2 units. So, the answer is C: The graph of \( f(x)=x^{2} \) should be horizontally shifted to the right by 6 units and vertically shifted up by 2 units. In the world of graphing, visualizing transformations is like moving from one party to another! Each transformation is a fun way to tour different coordinates—bumping the party left (horizontal shift), moving it up (vertical shift), or flipping it upside down (reflection). So put on your graphing shoes and get ready to dance!