This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

The emphasis in this task is on the progression of equations, from two that involve different values of the sales tax, to one that involves the sales tax as a parameter. It is designed to foster the habit of looking for regularity in solution procedures, so that students don't approach every equation as a new problem but learn to notice familiar types.

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The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

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College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.

The foundation of this lesson is constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans. Students are given three different DVD rental plans and asked to analyze each one to see if they could determine when the 3 different DVD plans cost the same amount of money, if ever. (7th/8th Grade Math)

We visualize complex numbers in the same way we visualize an ordered pair on a plane.

This task asks students to perform computations involving complex numbers using the given information.