Question: 14. List the intercepts of the graph. Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. Graph shape: two symmetric curves open upward and downward about the x-axis and y-axis, with one branch in the top half and one branch in the bottom half; position_hint = center. 15. Find the center $ (h, k) $ and radius $ r $ of the circle. Graph the circle. $ (x-5)^2 + (y-1)^2 = 3 $ Graph shape: blank coordinate plane with x- and y-axes, intended for plotting a circle centered at $ (5, 1) $ with radius $ \sqrt{3} $; position_hint = center.

1. Problem 14: Identify intercepts and symmetry of the graph described as two symmetric curves opening upward and downward about both axes. 2. Since the graph is symmetric about both the x-axis and y-axis, it is also symmetric about the origin. 3. Intercepts occur where the graph crosses the axes. Because the graph is symmetric about both axes, intercepts on x-axis and y-axis are symmetric. 4. Without an explicit equation, exact intercepts cannot be calculated, but the description implies intercepts at the origin or symmetric points. --- 5. Problem 15: Find the center and radius of the circle given by the equation $$ (x-5)^2 + (y-1)^2 = 3 $$. 6. The general form of a circle is $$ (x-h)^2 + (y-k)^2 = r^2 $$ where $ (h, k) $ is the center and $ r $ is the radius. 7. Comparing, we identify: $$ h = 5, \quad k = 1, \quad r^2 = 3 $$ 8. Therefore, the radius is: $$ r = \sqrt{3} $$ 9. The center is at $ (5, 1) $ and the radius is $ \sqrt{3} $. 10. This circle can be graphed on a coordinate plane with center at $ (5, 1) $ and radius $ \sqrt{3} \approx 1.732 $. Final answers: - Problem 14: The graph is symmetric about the x-axis, y-axis, and origin. - Problem 15: Center $ (5, 1) $, radius $ \sqrt{3} $.