Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus III
Topic: Vectors and Geometry of Space

Overview

Beyond planes, more 3D shapes surface (pun intended)! Quadratic surfaces are also called quadric surfaces or quadrics for short. They have general equation ax2+by2+cz2+2dx+2ey+2fz+2gxy+2hxz+2iyz+j=0 (where a, b, ..., j are constants). A quadric surface intersects every axes plane in a (possibly degenerate) conic section. Examples of quadratic surfaces include the cone, cylinder, ellipsoid, elliptic cone, elliptic cylinder, elliptic hyperboloid, elliptic paraboloid, hyperbolic cylinder, hyperbolic paraboloid, paraboloid, sphere, and spheroid.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 13.7.1 Find equation and graph (manually and electronically) a sphere and cylinder in R3
• 13.7.2 Identify a quadric surface from its equation or graph
• 13.7.3 Find the general equation of a given quadratic surface
• 13.7.4 Find the axis intercept points of a quadric surface
• 13.7.5 Find the trace of a quadric surface (ie, the xy-trace, xz-trace, and yz-trace)
• 13.7.6 Graph a quadric surface electronically

Terminology

Terms you should be able to define: quadric surface, all 12 quadrics hyperlinked in the overview above, trace, xy-trace, xz-trace, yz-trace