The functions f(x)=x^2 and g(x)=(1)/(2)(x-5)^2 are graphed on the same coordinate grid.Which statements are true? Select THREE correct answers. A. The graph of g is a vertical compression of the graph off. B. The graph of is a vertical stretch of the graph off. C. To create g f is translated 5 units to the left. D. To create g f is translated 5 units to the right. E. The vertex ofg is 3 units to the left of the vertex off. F. The vertex ofg is 5 units to the right of the vertex of f.

To determine which statements are true, we need to analyze the given functions and their graphs.<br /><br />Step 1: Analyze the function $f(x)=x^{2}$<br />The function $f(x)=x^{2}$ is a basic quadratic function. Its graph is a parabola that opens upwards with its vertex at the origin (0,0).<br /><br />Step 2: Analyze the function $g(x)=\frac {1}{2}(x-5)^{2}$<br />The function $g(x)=\frac {1}{2}(x-5)^{2}$ is a transformed quadratic function. The term $(x-5)$ indicates a horizontal translation of 5 units to the right, and the coefficient $\frac {1}{2}$ indicates a vertical compression by a factor of $\frac {1}{2}$.<br /><br />Step 3: Compare the graphs of $f(x)$ and $g(x)$<br />Based on the analysis in steps 1 and 2, we can conclude the following:<br />- The graph of $g(x)$ is a vertical compression of the graph of $f(x)$ by a factor of $\frac {1}{2}$.<br />- The graph of $g(x)$ is translated 5 units to the right compared to the graph of $f(x)$.<br />- The vertex of $g(x)$ is 5 units to the right of the vertex of $f(x)$.<br /><br />Therefore, the correct answers are:<br />A. The graph of g is a vertical compression of the graph off.<br />D. To create g f is translated 5 units to the right.<br />F. The vertex ofg is 5 units to the right of the vertex of f.