The graph shown in the picture is a hyperbola. It can be shown that the center lies on the line of symmetry. In this case, it can be seen that center of the hyperbola is at (3,-5). A hyperbola has an equation of x^2/a - y^2/b =1. a and b are the units between the two curves. a and b are both equal to 4. SInce the center is (3,-5), the equation of the parabola is (x-3)^2/4 - (y+5)^2/4 =1.