NONLINEAR SYSTEMS, CONIC SECTIONS, SEQUENCES, AND SERIES

College Algebra

Nonlinear Systems of Equations

Solving by eliminationApplications

Parabolas

Distance and midpoint formulasGeometric definition of parabolaDeveloping the equationParabolas in the form y = a(x - h)2 + KFinding the vertex, focus, and directrixAxis of symmetryChanging formsParabolas opening to the right or left

Circles

The equation of a circleEquations not in standard formSystems of equations

Ellipses and Hyperbolas

The ellipseThe hyperbola

Second-Degree Inequalities

Graphing a second-degree inequalitySystems of inequalities

Sequences

Sequences Finding a formula for the nth term

Series

Summation notationSeries Changing the index

Arithmetic Sequences and Series

Arithmetic sequencesArithmetic series

Geometric Sequences and Series

Geometric sequencesFinite geometric seriesInfinite geometric seriesApplications

Binomial Expansions

Some examplesObtaining the coefficientsThe binomial theorem