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 \( h(x) = (x-6)^{2} + 2 \) using transformations of \( f(x) = x^{2} \), we can analyze the changes step-by-step. **General Form of Quadratic Transformations:** \[ g(x) = a(x - h)^{2} + k \] - **\( h \)**: Horizontal shift. - If \( h > 0 \), the graph shifts **right** by \( h \) units. - If \( h < 0 \), the graph shifts **left** by \( |h| \) units. - **\( k \)**: Vertical shift. - If \( k > 0 \), the graph shifts **up** by \( k \) units. - If \( k < 0 \), the graph shifts **down** by \( |k| \) units. **Applying to \( h(x) = (x-6)^{2} + 2 \):** - **Horizontal Shift (\( h = 6 \))**: - Since \( h = 6 \) is positive, the graph shifts **right** by **6 units**. - **Vertical Shift (\( k = 2 \))**: - Since \( k = 2 \) is positive, the graph shifts **up** by **2 units**. **Conclusion:** To graph \( h(x) = (x-6)^{2} + 2 \), you should shift the graph of \( f(x) = x^{2} \) **right by 6 units** and **up by 2 units**. **Correct Answer:** **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.**