Analyzing Conics
This unit builds on knowledge of linear equations. The graph of a second-degree equation of the general form Ax^2+By^2+Cx+Dy+F=0 depends on the coefficients. From the general form, equations can be put into standard form. The standard-form equation can be used to classify and graph the conic section. Conics, such as circles, parabolas, ellipses, and hyperbolas, will be analyzed by slicing. This unit is leading to further study of graphs of second-degree equations that contain xy-terms. I n the future, it will be important to take a geometric description of a conic section and derive a quadratic equation representing it. In later courses, trigonometry and rotations will be used to classify and graph conic sections whose equations contain xy-terms.