Chapter 13 - Nonlinear Systems and the Conic Sections

The chapter begins with a look at nonlinear equations and how to solve nonlinear systems of equations by elimination. Then the parabola is investigated, with discussions of the geometric definition, how to develop an equation for a parabola given the focus and directrix, the special form y = a(x - h)² + k, the relationship between the equation and the vertex, focus, and directrix, the concept of axis of symmetry, and translation between the two forms for the equation of a parabola. The circle is then discussed, including development of the standard equation, equations that are not in standard form, and systems of equations that involve the equation of a circle. Finally, the ellipse and hyperbola are defined, discussed, and graphed.

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