How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

Explores quadratic functions using the graphing calculator. Discoveries are made graphically whereas hypotheses are proven algebraically. Includes traditional quadratics, other algebraic quadratics, nonpolynomial quadratics, transcendental quadratics, and proofs. (MKR)

Since 1995, astronomers have discovered over 100 known exoplanets--planets outside of the solar system--and determined their properties such as mass, orbital distance, size, and density. By using simple algebraic equations of physics, students can determine these properties as well. In this article, the author discusses an activity titled…

The students need not compute dependent values required in making line graphs but to teach the students the usage of graphing calculator to plot, calculating and graph linear equations, which are best suited to real world data. In this initial learning process, the teacher should give minimum support to the students in arriving at a solution as…

The mathematics students are given a task to understand the fundamentals of liner functions by analyzing the height of the football stadium bleachers, as studying mathematical relationships in real-world contexts can enhance a student's knowledge of mathematics. The study of the stadium seating problem helps students to understand quadratic,…

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

This analysis of information contents of documents (i.e., network of nodes which represent facts reported therein and their conceptual interconnections) yields a method for quantitative measurement of such content. Basic premises, calculation, salient features of the method, and information theories are discussed. Four references, graphic…

Shows how five points determine the formula of a conic section and uses the determinant as a computational device to find the coefficients in the formula. Uses symbolic, numerical, and graphical techniques. (Author/MKR)

Points of view analysis, as a way to deal with individual differences in multidimensional scaling, was largely supplanted by the weighted Euclidean model. It is argued that the approach deserves new attention, especially as a technique to analyze group differences. A streamlined and integrated process is proposed. (SLD)

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

The graphing of intricate curves and the fundamental theorem of algebra lead to a third discovery with microcomputers: Lagrange polynomials. Teaching suggestions for helping students to explore continuous change, interpolation, roots, and shifting and symmetry are presented, with a computer program listing. (MNS)

In two previous studies we investigated the non-routine problem-solving abilities of students just finishing their first year of a traditionally taught calculus sequence. This paper reports on a similar study, using the same non-routine first-year differential calculus problems, with students who had completed one and one-half years of traditional…

It has been found that students gain much greater insight into routine calculations with business formulas when such work is viewed in the light of graphing concepts. Ten problems are presented that illustrate how three specific objectives in a unit on graphing in a business mathematics course have been met. (MP)

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)